Lab+17+-+Simple+Pendulum

Lab 17 - Simple Pendulum

Procedure
 * 1) Pendulums were created from massless strings and weight sets suspended from a fixed point.
 * 2) For the Mass vs. Period test, 1 meter of string was used with 20g masses incrementally added with each trial with an initial amplitude of π/4 or 45˚.
 * 3) For the Amplitude vs. Period test, 1 meter of string and a 50g mass were used. The initial starting position for each of the 5 trials were π/3, π/4, π/6, π/12, and π/24.
 * 4) For the Length vs. Period test, a 50g mass was used with an initial amplitude of π/4. The lengths were changed from 1 meter to 0.5m to 0.25m.
 * 5) 10 cycles/periods were counted and timed.

Graphs

We know that the formula for the period of a simple pendulum (13.14) is T = 2π √(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. For the Mass vs. Period, we should expect a perfectly linear, horizontal correlation since neither length of the pendulum nor the acceleration due to gravity were changed. However, due to the inaccuracies and inability to time the periods accurately, a slightly negative correlation was found. It is believed that the difference in period time of approximately 0.02 seconds from the first to the last trial is sufficiently small enough to rule insignificant and, most importantly, close enough.

We know that the formula for the period of a simple pendulum (13.14) is T = 2π √(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. For the Amplitude vs. Period, we should expect the same as above for the same reasons. Since the period for a simple pendulum is not dependent upon the amplitude, we should have expected a horizontal trend line. This was not the case due to inaccuracies in measuring the periods along with trouble having the pendulum swing at higher amplitudes without grazing the surface it was near. This caused the more noticeable gap between the first and the last trials with a total difference of approximately 0.1 seconds.

We know that the formula for the period of a simple pendulum (13.14) is T = 2π √(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. For the Length vs. Period, we should expect that as L becomes larger or smaller, the period should lengthen or shorten, respectively. This is because the formula for the period of a simple pendulum is dependent upon the length (L) of the pendulum string and is, in fact, directly proportional to the square root of it. Should the pendulum string length decrease, the period should also decrease and vice versa if the string would be lengthened.