Question

If the displacement equation of a particle from its mean position is given as $y=0.2\sin (10\pi t+1.5\pi )\cos (10\pi t+1.5\pi )$ then, the motion of particle is

• A. Non-periodic
• B. Periodic but not SHM
• C. SHM with period 0.2 s
• D. SHM with period 0.1 s

Answer 1

The correct option is D SHM with period 0.1 s

Given,
$y=0.2\sin (10\pi t+1.5\pi )\cos (10\pi t+1.5\pi )$
$=0.1\sin 2(10\pi t+1.5\pi )$
$[\because \sin 2A=2\sin A\cos A]$
$=0.1\sin (20\pi t+3.0\pi )$
So, the motion of particle is SHM
Time period,
$T=\frac{2\pi }{\omega }=\frac{2\pi }{20\pi }=\frac{1}{10}=0.1s$