Question

At what point in a pendulum’s swing is the tangential force on the bob zero? How do you know?

Answer 1

We have for the osscillation of the simple pendulum(SHM),

The displacement equation of bob as,

on differentiating the displacement,we get velocity of the bob as,

On differentiating the velocity function with respect to time,We ger Acceleration of the bob as,

So,the tangential force on the bob,

ie,

For the instant where the force equals to zero,

So,

Implies,

,Where n=1,2,3....

We have angular velocity of the osscillation,

Where, is the time period of the osscllation.

So,

ie,

So,the tangential force on the bob of the simple pendulum osscillation will be zero at times,,where n=1,2,3..

We have displacement,

For,

(ie pendulum or bob at the mean position)

So,the tangential force on the bob of the pendulum will be zero at the instant when the bob is at the mean position () during osscillation(SHM).