First slide

Simple hormonic motion

Question

The displacement of a particle from its mean position (in metre) is given by $y = 0.2 \sin (10 πt + 1.5 π) \cos (10 πt + 1.5 π)$ . The motion of particle is

Moderate

A

Periodic but not S.H.M.
B

Non-periodic
C

Simple harmonic motion with period 0.1 s
D

Simple harmonic motion with period 0.2 s

Solution

$y = 0.2 \sin (10 πt + 1.5 π) \cos (10 πt + 1.5 π)$
= $0.1 \sin 2 (10 πt + 1.5 π)$
= $0.1 \sin (20 πt + 3.0 π) [∵ \sin 2 A = 2 \sin A \cos A]$
$∴ Time period, T = \frac{2 π}{ω} = \frac{2 π}{20 π} = \frac{1}{10} = 0.1 \sec$

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