Q.

Starting from the origin a body oscillates simple harmonically with period of 2 s. After what time will its kinetic energy be 75% of the total energy

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a

1 /6 s

b

1 /4 s

c

1 / 3 s

d

1/12 s

answer is A.

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Detailed Solution

The kinetic energy of a body undergoing S.H.M. is given by   K.E. =12mω2A2cos2⁡ωt  or   (K.E.) max=12mω2A2According to given problem K.E.=(75/100)(K.E.)max∴ 12mω2A2cos2⁡ωt=7510012mω2A2  or  cos⁡ωt=±3/2  or  Ï‰t=π6  or  2πT×t=π6  or  t=T12=16s
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