Question

A body of mass $1 kg$ is executing simple harmonic motion. Its displacement $y(c m)$ at $t$ seconds is given by $y=6 \sin \left(100 t+\frac{\pi}{4}\right)$. Its maximum kinetic energy is:

• A. $6\, J$
• B. $18\, J$
• C. $24\, J$
• D. $36\, J$

Answer 1

Answer: (B)

$y = A \sin (\omega t +\phi)$
$A =6 \,cm$
$m =1\, kg$
$\omega=100\, rad / \sec$
$KE _{\max }=\frac{1}{2} m \omega^{2} A ^{2}$
$=\frac{1}{2} \times 1 \times(100)^{2} \times\left(10^{-2}\right)^{2} \times 6^{2}$
$=18\, J$