Question

The equation of a particle executing simple harmonic motion is given by $x=\sin \pi\left(t+\frac{1}{3}\right) m$. At $t =1 s$, the speed of particle will be (Given : $\pi=3.14$ )

• A. $0 \,cm \,s ^{-1}$
• B. $157 \, cm \, s ^{-1}$
• C. $272 \,cm \, s ^{-1}$
• D. $314 \, cm \,s ^{-1}$

Answer 1

Answer: (B)

$x =\sin \pi\left( t +\frac{1}{3}\right)$
$x =\sin \left(\pi t +\frac{\pi}{3}\right)$
$V =\frac{ dx }{ dt }=\cos \left(\pi t +\frac{\pi}{3}\right) \pi$
$=-\pi \times \frac{1}{2}=157\, cm / s$