Question

An object of mass $0.5 \,kg$ is executing simple harmonic motion. It amplitude is $5 \,cm$ and time period $( T )$ is $0.2 \,s$. What will be the potential energy of the object at an instant $t=\frac{T}{4} s$ starting from mean position. Assume that the initial phase of the oscillation is zero.

• A. $0.62\, J$
• B. $6.2 \times 10^{-3} \,J$
• C. $1.2 \times 10^{3} \,J$
• D. $6.2 \times 10^{3} \,J$

Answer 1

Answer: (A)

$T=2 \pi \sqrt{\frac{m}{k}}$
$0.2=2 \pi \sqrt{\frac{0.5}{k}}$
$k=50 \pi^{2}$
$\approx 500$
$x=A \sin (\omega t+\phi)$
$=5\, cm \sin \left(\frac{\omega T}{4}+0\right)$
$=5 \,cm \sin \left(\frac{\pi}{2}\right)$
$=5 \,cm$
$P E=\frac{1}{2} k x^{2}$
$=\frac{1}{2}(500)\left(\frac{5}{100}\right)^{2}$
$=0.6255$