A body is performing simple harmonic motion. Then its

Options

A. 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. average total energy per cycle is equal to half of its malximum kinetic energy.
D. None of these.

Answer

B

Explanation

When a body performs `S.H.M.` total energy of the body remain constant and kinetic energy of the body is maximum at mean position its maximum value is equal to total oscillation energy of the body .Hence average total oscilation energy per cycle is equal its the maximum `K.E.` of the body hence (a) is connect Obviously (c) is wrong
If amplitude of oscillations is equal to a and angular frequency is to then maximum velocity of the body will be equal to a as and it varius according to sine over a completed cycle will be equal to `(1)/(sqrt(2)) a omega`
Avarage `K.E. = (1)/(2) mv_(max)^(2) = (1)/(4) ma^(2) a omega`
which is half of maximum `K.E.`