First slide

Simple hormonic motion

Question

A pendulum oscillates in a vertical plane. When the bob is at extreme position, its acceleration is $5 m / s^{2}$ . If $g = 10 m / s^{2}$ , angular amplitude of oscillation of the pendulum is

Moderate

Solution

At extreme position A, tangential unbalanced force acting on the bob is $mg sinϕ$ .
So acceleration at this position $a = m g \sin \frac{ϕ}{m} = g \sin ϕ$
$∴ G i v e n 10 \sin ϕ = 5 \Rightarrow \sin ϕ = \frac{1}{2} \Rightarrow ϕ = 30^{o}$

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