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.
Correct Option: 1
Solution:
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
$0.2=2 \pi \sqrt{\frac{0.5}{k}}$
$\mathrm{k}=50 \pi^{2}$
$\approx 500$
$x=A \sin (\omega t+\phi)$
$=5 \mathrm{~cm} \sin \left(\frac{\omega \mathrm{T}}{4}+0\right)$
$=5 \mathrm{~cm} \sin \left(\frac{\pi}{2}\right)$
$=5 \mathrm{~cm}$
$\mathrm{PE}=\frac{1}{2} \mathrm{kx}^{2}$
$=\frac{1}{2}(500)\left(\frac{5}{100}\right)^{2}$
$=0.6255$