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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a
π2ma2v2
b
14ma2v2
c
4π2ma2v2
d
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