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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(12) 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 14mv20
Let equation of SHM is, x=Asinωt

Then velocity of particle is given by, v=dxdt=Aωcosωt

Maximum velocity, vo=Aω

Let at time t, particle is at distance 12 times the A

x=A2=Asinωt

ωt=π4

At time t, velocity is, v=Aωcosπ4=vo2

Kinetic energy =12mv2
K.E.=12m(vo2)2

K.E.=14mv2o

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