First slide

Simple hormonic motion

Question

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 $20 m s^{- 2}$ at a distance of 5 m from the mean position. The time period of oscillation is

Easy

A

$2 π s$
B

$π s$
C

$2 s$
D

$1 s$

Solution

Magnitude of acceleration of a particle moving in a SHM is
$| a | = ω^{2} y; where y is amplitude.$
$\Rightarrow 20 = ω^{2} (5) \Rightarrow ω = 2 rad s^{- 1}$
$∴$ Time period of oscillation
$T = \frac{2 π}{ω} = \frac{2 π}{2} = π s e c$

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