Pendulum versus Harmonic Oscillator
φ0 =
0.2
rad
0π





Three masses are suspended each on a massless rod of length L. They can rotate freely around the black pivotal point in the drawing, without any friction. The green one is a pendulum that always start from an angle of 0.2 rad.
The blue and the red one can start from any angle.
All are released at the same time, with zero initial velocity.
Due to the small initial angle, the green one is virtually a harmonic oscillator.
The blue one shows the motion of a harmonic oscillator with \( \omega_0 = \sqrt{ \frac{g}{L}} \), which does not correctly describe a pendulum for larger angles.
The red circle shows the (numerical) solution of the pendulum.
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