Question

The displacement of a particle from its mean position (in metre) is given by $y=0.2 \, sin (10\pi t+1.5 \pi) cos (10\pi t+1.5 \pi)$ The motion of the particle is

• A. periodic but not SHM
• B. non periodic
• C. simple harmonic motion with period 0.1 s
• D. simple harmonic motion with period 0.2 s

Answer 1

Answer: (C)

simple harmonic motion with period 0.1 s

Answer 2

Given $y=0.2 \, sin (10\pi t+1.5 \pi) cos (10\pi t+1.5 \pi)$ $\, \, \, \, \, \, \, \, y=0.1 \, sin 2(10\pi t+1.5\pi)$ \hspace30mm[using 2sin A cos A = sin 2A] $y = 0.1 sin (20\pi t + 3\pi)$ This equation represents simple harmonic motion of angular frequency 20$\pi$ $\therefore \, \, \, \, Time \, period \, T =\frac{2\pi}{\omega}=\frac{2\pi}{20\pi}$ $\, \, \, \, \, \, \, =\frac{1}{10}=0.1 s$