Simple Pendulum Essay Example

L = Lo - Li
If a small angle is assumed, the period and the frequency of the pendulum become independent of the amplitude of the initial angular displacement. Every simple pendulum should possess the same period despite their initial angle as well as their masses. A simple pendulum’s period is independent on the initial angular displacement or the mass, however, it is dependent on the string’s length, L as well as the gravitational field strength’s value g. A simple pendulum’s motion can be compared to that of a simple harmonic motion so that we can have the equation for the angular displacement which is

This motion is similar to the same form as that of a motion of a mass in a spring.

This can also be compared to motion of a mass in a spring.
A pendulum’s frequency is given by
But since Period T=1f it then becomes

Therefore, the length, L will be

L = gT²/4∏²
The difference between the two lengths, L, will be Lo - Li on the first method and gT²/4∏²on the second method. To obtain a graph, we will plot period against the length since they are the variables for the formula then using the power law y = Ax the equation of the pendulums period will be obtained by substitution of the Period T with Y and x with L
The experimental value of the slope is expected to be between 0.505 and 0.513
Using an example where the period is 0.6383 and the length is 0.10 m
Using the second formula L= gT²/4∏²
= 9.8(0.6383) ²/4∏²
= 3.992/39.4784
= 0.1011 M
The difference in the values is thus 0.1011- 0.10 = 0.0011 m