A body is performing `SHM`, 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. mean velocity over a complete cycle is equal to `(2)/(pi)` times of its maximum velocity
D. root meqan square velocity is `(1)/(sqrt(2))` times of its maximum velocity

Answer

A, B, D

Explanation

In case of `S.H.M.`, average total energy per cycle
=Maximum kinetic energy `(K_(0))`
=Maximum potential energy `(U_(0))`
Average `KE` per cycle `= (0+K_(0))/(2) = (K_(0))/(2)`
Let us find velocity of the particle,
`v = (dx)/(dt) = (d)/(dt) (a sin omegat) = a omega cos omegat`
Mean velocity over a complete cycle,
`v_(mean) = (int_(theta)^(2pi)omegaa cos theta d theta)/(2pi)=(omegaa[sin theta]_(0)^(2pi))/(2pi) =0`
So, `v_(mean) != (2)/(pi) v_(max)`
Root mean square speed,
`v_(rms) = sqrt((v_(min)^(2)+v_(max)^(2))/(2)) =sqrt((0+v_(max)^(2))/(2))`
`v_(rms) = (1)/(sqrt(2)) v_(max)`