A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is at a distance of 5 m from the mean position. The time period of oscillation

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Solution

Q.
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20$ ${ms}^{- 2}$ at a distance of 5 m from the mean position. The time period of oscillation is [2018]

1 $2 π$ $s$

2 $π$ $s$

3 $2$ $s$

4 $1$ $s$

Ans.
(2)

Magnitude of acceleration of a particle moving in a S.H.M. is, $| a |$ $= ω^{2} y, where y is amplitude .$

$\Rightarrow 20 = ω^{2} (5) \Rightarrow ω = 2 {rad s}^{- 1}$

$∴$ $Time period of oscillation, T = \frac{2 π}{ω} = \frac{2 π}{2} = π s$

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