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Q.

In simple harmonic motion how many times potential energy is equal to kienetic energy during one complete period?

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a

1

b

2

c

8

d

4

answer is D.

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Detailed Solution

If frequency of oscillation is f, then frequency of potential or kinetic energy is 2f. Now, K=12mω2A2sin2ωt and U=12mω2A2cos2ωtWhen K=U, 12mω2A2sin2ωt=12mω2A2cos2ωt⇒tanωt=±1, ⇒ωt=π4,3π4,5π4,7π4So in a cycle K=U, at t=π4ω,3π4ω,5π4ω,7π4ω.
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