Example 1: Simple pendulum A pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion |
angle / degree | T /s | T_theory / s | error = ( T - T_theory)/ T*100 % |
5 | |||
10 | |||
15 | |||
20 | |||
30 | |||
40 | |||
50 | |||
60 | |||
70 | |||
80 | |||
90 |
$ \theta \approx 10 $ degrees for error of $ \frac {2.010-2.006}{2.010}= 0.2 %$, depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical.
Motion approximates simple harmonic motion when the angle of oscillation is small.
Motion approximates SHM when the spring does not exceed limit of proportionality during oscillations.