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 | $e$ |
05 | |||
10 | |||
15 | |||
20 | |||
30 | |||
40 | |||
50 | |||
60 | |||
70 | |||
80 | |||
90 |
With the evidences
collected or otherwise, suggests what the conditions of which the
angle of oscillation can the actual period T be approximated to
theoretical period such that T ≈ $$
angle θ ≈ 10 degrees for $e$
Motion approximates simple harmonic motion when the angle of
oscillation is small < 10 degrees..
Motion approximates SHM when the spring does not exceed limit of
proportionality during oscillations.
Astronomical applications of the Small Angle Approximation
http://youtu.be/BRbCW2MsL94?t=2m16s This video shows many pendulums that goes in phase and out of phase with each other pendulum to creating a visually stunning effect.