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A body is oscillating simple harmonically with a period T = 2 s. How much time would it take for its kinetic energy to decrease from $K_{max}$ to 75 % of $K_{max}$ ?

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Correct option is D

K=12mv2=m2A2ω2cos2⁡(ωt) and Kmax=mA2ω22 Given that K=0.75Kmax⇒cos⁡(ωt)=32⇒ωt=π6⇒2πTt=π6. Simplifying this we get t=T12=212=16s

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A body is oscillating simple harmonically with a period T = 2 s. How much time would it take for its kinetic energy to decrease from Kmax to 75 % of Kmax ?

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A body is oscillating simple harmonically with a period T = 2 s. How much time would it take for its kinetic energy to decrease from $K_{max}$ to 75 % of $K_{max}$ ?