Ncert Exercises & Solutions

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

Hint: For SHM, the displacement of the pendulum should be small.

Step 1: Find the condition for SHM.

Consider the diagram of a simple pendulum.

The bob is displaced through an angle

θ

shown.

The restoring torque about the fixed point O is,

τ = - m g \sin θ

θ

is small angle in radians, then sin

θ \approx θ

\Rightarrow τ \approx - m g θ \Rightarrow τ \propto (- θ)

Hence, the motion of a simple pendulum is SHM for small of oscillations.