Question

Why is amplitude of oscillation small?

Answer 1

Explanation,

1. If we consider a pendulum, we can see simple harmonic motion in it.
2. Time period does not depend on amplitude.
3. The equation of motion for a simple pendulum: is $\ddot{\theta }=\frac{g}{l}\sin \theta$
4. $T=2\pi \sqrt{\left(\frac{L}{g}\right)}$, where L is the length of the string in the pendulum and T is its time period.
5. So if the amplitude value$\ddot{\theta }$ is kept small, then the value $\sin \theta$ is very close to$\theta$, then the oscillations are smooth as the time period is independent of amplitude.

Hence, the amplitude of oscillation is small.