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

Question

If the displacement equation of a particle from its mean position is given as y=0.2 sin (10 π t+1.5 π) cos (10 π t+1.5 π) 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

Tardigrade Admin · Accepted Answer

Given, y=0.2 sin (10 π t+1.5 π) cos (10 π t+1.5 π) =0.1 sin 2(10 π t+1.5 π) [ sin 2 A=2 sin A cos A] =0.1 sin (20 π t+3.0 π) So, the motion of particle is SHM Time period, T=(2 π/ω)=(2 π/20 π)=(1/10)=0.1 s

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

non-periodic

periodic but not SHM

SHM with period 0.2 s

SHM with period 0.1 s

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

Q. If the displacement equation of a particle from its mean position is given as y=0.2sin(10πt+1.5π)cos(10πt+1.5π) then, the motion of particle is