Question

A body of mass $2\text{kg}$ is executing simple harmonic motion. Its displacement $y\text{(in cm)}$ at $t$ seconds is given by $y=6\sin (200t+\frac{\pi }{6})$. Find its maximum kinetic energy.

• A. $144\text{kJ}$
• B. $12\text{J}$
• C. $48\text{kJ}$
• D. $144\text{J}$

Answer 1

The correct option is D $144\text{J}$

Given,
mass of body $\left(m\right)=2\text{kg}$
Displacement $y=6\sin (200t+\frac{\pi }{6})$
Comparing with, $y=A\sin (\omega t+\varphi )$
$A=6\text{cm},\omega =200\text{rad/s},\varphi =\frac{\pi }{6}$
Maximum kinetic energy $\left({\text{KE}}_{max}\right)=\frac{1}{2}m{\omega }^2{A}^2$
$=\frac{1}{2}\times 2\times (200{)}^2\times (6\times {10}^{-2}{)}^2$
$=144\text{J}$