ABurkholder+Lab+16

Pendulum Lab Purpose: This lab will study which variables affect the period of a simple pendulum lab.

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. Hypothesis: 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. Apparatus: Procedure: Part 1: 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. Part 2: 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. Part 3: 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.
 * String (1.25m)
 * Hanging mass set (1)
 * Stopwatch (1)

Data: Table 1
 * ** Change in Period Due to Change in Mass ** ||
 * ** Trial ** || ** Mass (g) ** || ** Cycles ** || ** Time ** || ** Period (s/cycle) ** ||
 * ** 1 ** || 50 || 5 || 10.39 || 2.08 ||
 * ** 2 ** || 55 || 5 || 10.12 || 2.02 ||
 * ** 3 ** || 60 || 5 || 10.15 || 2.03 ||
 * ** 4 ** || 65 || 5 || 9.63 || 1.93 ||
 * ** 5 ** || 70 || 5 || 10.32 || 2.06 ||

Table 2
 * ** Change in Period Due to Change in Amplitude ** ||
 * ** Trial ** || ** Amplitude (cm) ** || ** Cycles ** || ** Time ** || ** Period (s/cycle) ** ||
 * ** 1 ** || 2 || 5 || 10.38 || 2.08 ||
 * ** 2 ** || 4 || 5 || 10.30 || 2.06 ||
 * ** 3 ** || 6 || 5 || 10.75 || 2.15 ||
 * ** 4 ** || 8 || 5 || 10.87 || 2.17 ||
 * ** 5 ** || 10 || 5 || 10.65 || 2.13 ||

Table 3 Analysis: 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. 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).
 * ** Change in Period Due to Change in Length ** ||
 * ** Trial ** || ** Length (cm) ** || ** Cycles ** || ** Time ** || ** Period (s/cycle) ** ||
 * ** 1 ** || 100 || 5 || 10.06 || 2.01 ||
 * ** 2 ** || 90 || 5 || 9.72 || 1.94 ||
 * ** 3 ** || 80 || 5 || 9.19 || 1.84 ||
 * ** 4 ** || 40 || 5 || 8.42 || 1.68 ||
 * ** 5 ** || 50 || 5 || 8.15 || 1.63 ||