Question

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

• A. periodic but not S.H.M
• B. non-periodic
• C. simple harmonic motion with a period $0.1 \, s$
• D. simple harmonic motion with a period $0.2s$

Answer 1

Answer: (C)

$y=0.2sin \left(10 \pi t + 1.5 \pi \right)cos ⁡ \left(\right.10\pi t+1.5 \, \pi \left.\right) \, $
$=0.1sin 2 \left(\right.10\pi t+1.5\pi \left.\right) \, $
$\left[\because sin 2 A = 2 \, sin A \, cos A\right]$
$=0.1sin \left(20 \pi t + 3.0 \pi \right)$
$\therefore $ Time period $T=\frac{2 \pi }{\omega }=\frac{2 \pi }{20 \pi }=\frac{1}{10}=0.1 \, s$