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Question

A particle undergoing SHM has the equation x=Asin(ωt+ϕ), where x represents the displacement of the particle. The kinetic energy oscillates with time period

A
2πω
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B
πω
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C
4πω
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D
None of these
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Solution

The correct option is B πω
For a particle executing SHM, starting from mean position (x=0) the displacement of the particle is given by
x=asinωt
For one complete oscillation, time period is T=2πω

Kinetic energy of the particle executing SHM is given by
K=12kA2cos2ωt=14kA2(1+cos2ωt)
we can conclude that, kinetic energy oscillates with frequency of 2ω.

So, for one complete oscillation, kinetic energy varies with time as
T=2π2ω=πω
Thus, option (b) is the correct answer.

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