BITSAT 2018 Paper

The kinetic energy of a particle executing S.H.M. is given by
K =

1

2

ma2ω2sin2ωt
Now, average K.E. = < K > = <

1

2

mω2a2sin2ωt >
=

1

2

mω2a2 < sin2 ωt >
=

1

2

mω2a2(

1

2

) (Since < sin2 θ > =

1

2

)
=

1

4

mω2a2 =

1

4

ma2(2πv)2 (Since ω 2πv)
or < K > = π2ma2v2