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Questions  

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

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

detailed solution

Correct option is C

y = 0.2 sin(10πt+1.5π)cos(10πt+1.5π)   = 0.1 sin 2(10πt + 1.5 π)    = 0.1 sin(20πt+ 3.0π)[∵ sin 2A = 2 sin A cos A]∴  Time period, T = 2πω = 2π20π = 110 = 0.1 sec

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