A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is:

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π2ma2v2

14ma2v2

4π2ma2v2

2π2ma2v2

answer is A.

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Detailed Solution

x=A cos ωt⇒v=dxdt=-Aω sin ωt KE=12mv2=12mA2ω2sin2ωt Average KE=12mA2ω2=12mA2ω2×12 =π2ma2v2

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