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Question

A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is

A
v/2
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B
v
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C
2v
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D
Zero
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Solution

The correct option is C 2v

It is given that, the a particle execute SHM with frequency v. The equation of particle executing SHM is

x=Asinωt

Velocity of particle is

v=dxdt

v=ddt(Asinωt)

v=Aωcosωt

So, the kinetic energy is:

K=12mv2=12m(Aωcosωt)2=12mω2A2cos2ωt

K=12mA2ω2(1+cos2ωt2)

K=14mω2A2(1+cos2ωt)

So, from equation the frequency of oscillation of kinetic energy is

ωK=2ω

Frequency of oscillation of kinetic energy is double as that of oscillation of particle.


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