Q. 17

# A body is performing S.H.M. Then itsA. average total energy per cycle is equal to its maximum kinetic energy.B. average kinetic energy per cycle is equal to half of its maximum kinetic energy.C. mean velocity over a complete cycle is equal to times of its maximum velocity.D. root mean square velocity is times of its maximum velocity.

Consider SHM,

Where A is the amplitude and is the angular frequency

Now velocity is given as,

Max velocity is given as, ----(1)

mean velocity ---(2)

square mean velocity

solving this we get, ---(3)

thus from equation (2) we can say that option c is incorrect and from equation (3) we can say that option (d) is correct

Now the instantaneous potential energy,

Where

---(4)

Total kinetic energy in SHM s given as,

---(5)

Average kinetic energy

Solving the above we get, ---(6)

Similarly,

Average potential energy

Solving the above we get, ----(7)

And average total energy

---(8)

Max kinetic energy ----(9)

And max potential energy ---(10)

Comparing equation (8) and (9) we see option a is correct.

Comparing equation (9) and (6) we see option b is also correct.

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