Question

if the period of oscillation of particle performing simple harmonic motion is 8 sec, then the frequency of its kinetic energy will be????
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Answer 1

frequency of kinetic energy = 16 sec

kinetic energy is given by, K.E = 1/2 mv²

for simple harmonic motion,

v = dy/dt = Awcos(wt + Φ) [ where y = sin(wt + Φ) is standard equation of shm ]

so, K.E = 1/2 mA²w²cos²(wt + Φ)

= 1/4 mw²A²[1 + cos2(wt + Φ)] [ we know , cos²x = (1 + cos2x)/2]

hence, frequency of kinetic energy is two times the frequency of simple harmonic wave.

given frequency of simple harmonic motion is 1/8sec [frequency = 1/time period ] then, frequency of its kinetic energy is 2 × 1/8 = 1/4 sec.

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Answer 2

$\huge\bold\purple{Answer:-}$

frequency of kinetic energy = 16 sec

hence, frequency of kinetic energy is two times the frequency of simple harmonic wave. given frequency of simple harmonic motion is 1/8sec [frequency = 1/time period ] then, frequency of its kinetic energy is 2 × 1/8 = 1/4 sec.