Question

How do I experimentally determine a mathematical relationship between period and amplitude, when using simple harmonic motion and a pendulum in a lab setting? We recorded values for amplitude, length of the pendulum and period. An example of the data collected :

Amplitude/Period

5 deg / 1.524 sec

10 deg / 1.532 sec

15 deg / 1.538 sec, etc...

The period stays roughly the same all the way up to 40 degrees. Is it as simple as graphing these data points and finding a line of best fit?

Answer 1

Actually amplitude is the extreme position of a pendulum in simple harmonic motion. The amplitude certainly does affect the period, but for sufficiently small amplitudes, say less than 5°, it is a good approximation to say that the period does not depend on the amplitude.

As we know for SHM , Period is given as

T = 2pi sqrt (L/g)

However,  For larger amplitudes, the period will be larger than this equation predicts. so we can say, for larger amplitude, time period will vary on a greater scale.

Yes you can try drawing a best fit line however do this for larger amplitudes where there is considerable difference between two time period readings