Question

A body of mass $1kg$ is executing simple harmonic motion (SHM). Its displacement $y$ (in $cm$ ) at time $t$ given by $y=\left[6\sin \left(100t+\frac{\pi }{4}\right)\right]cm$. Its maximum kinetic energy is

• A. $1.8J$
• B. $18J$
• C. $180J$
• D. $0.18J$

Answer 1

Answer: (B)

Given, mass of body, $m=1kg$
Displacement equation of SHM,
$y=\left[6\sin \left(100t+\frac{\pi }{4}\right)\right]cm$
$\text{ Let }{v}_y=\text{ velocity Hence, }{v}_y=\frac{dy}{dt}$
$v_y=\frac{d}{dt}\left[6\sin \left(100t+\frac{\pi }{4}\right)\right]$
$=6\times 100\cos \left(100t+\frac{\pi }{4}\right)$
$=600\cos \left(100t+\frac{\pi }{4}\right)cm{s}^{-1}$
$=6\cos \left(100t+\frac{\pi }{4}\right)m{s}^{-1}$
Maximum velocity, ${\left(v_y\right)}_{\max }=6m/s$
$\therefore$ Maximum kinetic energy,
$K_{\max }=\frac{1}{2}m{\left(v_y\right)}_{\max }^2$
$=\frac{1}{2}\times 1\times 6^2$
$=\frac{1}{2}\times 1\times 36$
$=18J$