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Question

# The maximum speed of a particle of mass executing SHM is υo. What is the kinetic energy of the particle ' when it is at distance(1√2) times the amplitude form its mean position?

A
12mv20
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B
13mv20
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C
14mv20
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D
None of the above
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Solution

## The correct option is C 14mv20Let equation of SHM is, x=AsinωtThen velocity of particle is given by, v=dxdt=AωcosωtMaximum velocity, vo=AωLet at time t, particle is at distance 1√2 times the Ax=A√2=Asinωt ωt=π4At time t, velocity is, v=Aωcosπ4=vo√2Kinetic energy =12mv2K.E.=12m(vo√2)2K.E.=14mv2o

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