LVang+-+L17+-+Simple+Pendulum+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 20 March 2012 Performed On: 15-16 March 2012 Lab Partners: Andrew Burkholder, Olivia Pfautz, Lue Vang

**Simple Pendulum Lab ** This lab will study which variables affect the period of a simple pendulum lab.
 * __Purpose: __**

 **__Background:__**  A simple pendulum is a pendulum in which a mass is hung on the end of a piece of string. If you hold the string vertically and pull the mass a certain angle from its vertical, it will oscillate back and forth in a simple harmonic motion. A period (T) is the time required for simple harmonic motion to complete one cycle. Amplitude (A) is object’s the magnitude of max displacement, which will be measured with the angle of displacement of the pendulum.

 Since the formula for the period of a spring system is T = 2π(L/g)^(1/2), changing the mass or amplitude of the system will not change the period of the pendulum system, but changing the length (L) of the pendulum, however, will change the period. As length (L) increases, the period will increase.
 * __Hypothesis: __**

 **__Apparatus:__**
 * String (1.25m)
 * Hanging mass set (1)
 * <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Stopwatch (1)

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Part 1: <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hang the string on an elevated prong. Then, attach the mass to the bottom of the string so that there is a length of 1m between the top of the string and the mass at the bottom. Move the pendulum to an amplitude of 15° from the equilibrium and let it go. Record the time necessary to complete 5 cycles and calculate the period. Conduct the procedure starting with a mass of 50g and increasing it by intervals of 5g each trial for five trials. Record the periods for each mass.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Procedure: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> Part 2: <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hang the string on an elevated prong. Then, attach the mass to the bottom of the string so that there is a length of 1m between the top of the string and the mass at the bottom. Move the pendulum to an amplitude of 15° from the equilibrium and let it go. Record the time necessary to complete 5 cycles and calculate the period. Conduct the procedures starting with an amplitude of 15° and increase it by intervals of 5° for five trials.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Part 3: <span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Hang the string on an elevated prong. Then, attach the mass to the bottom of the string so that there is a length of 1m between the top of the string and the mass at the bottom. Move the pendulum to an amplitude of 15° from the equilibrium and let it go. Record the time necessary to complete 5 cycles and calculate the period. Conduct the procedures starting with an length (L) of 100cm and decreasing it by intervals of 10cm for five trials.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> **__Data:__** <span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 1.0


 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Mass ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Mass (g) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">50   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.39   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.08   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">55   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.12   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.02   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">60   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.15   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.03   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">65   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.63   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.93   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">70   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.32   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.06   ||

<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 2.0


 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Amplitude ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Amplitude (cm) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.38   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.08   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.30   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.06   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">6   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.75   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.15   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.87   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.17   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.65   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.13   ||

<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 3.0


 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Length ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Length (cm) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">100   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.06   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.01   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">90   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.72   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.94   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">80   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.19   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.84   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">40   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8.42   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.68   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">50   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8.15   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.63   ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Graphs 1.0 and 2.0 indicate that changing the mass and/or amplitude of the pendulum does not affect its period because the correlation coefficient is practically zero. It’s also eminent that the slope is almost horizontal.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Analysis: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Graph 3.0 shows a slight positive slope, suggesting that changing the length (L) of the pendulum does affect the period: as the length (L) increases, the period (T) increases linearly.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">All in all, the results of this lab agree with the period equation for simple pendulums: T = 2π(L/g)^(1/2). As length (L) increases, period (T) increases linearly. As for mass (m) and amplitude, they’re not in the equation, and likewise, changing them do not affect the period (T).

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;"> The hypothesis is supported: Graphs 1.0 and 2.0 indicate that changing the mass and/or amplitude of the pendulum does not affect its period because the correlation coefficient is practically zero. It’s also eminent that the slope is almost horizontal. Graph 3.0 shows a slight positive slope, suggesting that changing the length (L) of the pendulum does affect the period: as the length (L) increases, the period (T) increases linearly.
 * __<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Conclusion: __**

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Like the analysis says, the pattern follows the equation of T = 2π(L/g)^(1/2), the equation for the period of a simple pendulum.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">This lab is done relatively accurately. The only major way to realistically improve accuracy is to add more trials for each mass, amplitude, and/or length run.

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Even though the correlation coefficient for Graph 3.0, is low, the data Table 3.0 shows that changing length affects the period. The low correlation coefficient is likely due to the small increments of change. <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;"> <span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 1.0 <span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 2.0 <span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12.0pt; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman";">Table 3.0
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Mass ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Mass (g) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">50   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.39   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.08   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">55   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.12   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.02   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">60   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.15   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.03   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">65   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.63   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.93   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">70   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.32   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.06   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Amplitude ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Amplitude (cm) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.38   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.08   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.30   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.06   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">6   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.75   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.15   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.87   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.17   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.65   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.13   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Change in Period Due to Change in Length ** ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Trial ** ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Length (cm) **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Cycles **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Time **  ||  **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Period (s/cycle) **  ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">100   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">10.06   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2.01   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">2 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">90   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.72   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.94   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">3 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">80   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">9.19   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.84   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">4 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">40   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8.42   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.68   ||
 * **<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5 ** ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">50   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">5   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">8.15   ||  <span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">1.63   ||