An object of mass 0.5 , kg is executing simple harmonic motion. I… - Vidyadip

MCQ

An object of mass $0.5\, {kg}$ is executing simple harmonic motion. Its 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. (In ${J}$)

A
$1.2$
✓
$0.62$
C
$6.2$
D
$620$

✓

Answer

Correct option: B.

$0.62$

b
by using formula of time period

$T=2 \pi \sqrt{\frac{m}{k}}$

$0.2=2 \pi \sqrt{\frac{0.5}{k}}$

$k=50 \pi^{2}$

$\approx 500$

$x=A\, \sin (\omega t+\phi)$

$=5\, c m\, \sin \left(\frac{\omega t}{4}+0\right)$

$=5\, {cm} \sin \left(\frac{\pi}{2}\right)$

$=5 \,{cm}$

$P E=\frac{1}{2} k x^{2}$

$=\frac{1}{2}(500)\left(\frac{5}{100}\right)^{2}$

$=0.6255$

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