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Question
When will the motion of a simple pendulum be simple harmonic?
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Solution
Simple pendulum performs angular S.H.M. Consider the bob of a simple pendulum is displaced through an angle θ shown. Q
The restoring torque about the fixed point O is τ = mgl sinθ
If θ is the small angle in radians, then sin θ = 0
⇒ mglθ
In vector form τ ∝ θ
Hence, the motion of a simple pendulum is SHM for small angles of oscillations.
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