Question

When will the motion of a simple pendulum be simple harmonic?

Answer 1

Formula used: $\tau =-mgL\sin \theta$

For Simple pendulum



Restoring torque

$\tau =-mgL\sin \theta$

For simple harmonic motion $\sin \theta \cong \theta$

$\tau =-mgL\theta$

$\tau \propto -\theta$


Final Answer: When the bob of the pendulum is displaced from the mean position so that $\sin \theta \cong \theta .$