In forcd oscillation of a particle, the amplitude is maximum for a frequency `omega_(1)` of the force, while the energy is maximum for a frequency `omega_(2)` of the force. What is the relation between `omega_(1)` and `omega_(2)` ?

Options

A. `omega_(1) lt omega_(2)`
B. `omega_(1) gt omega_(2)`
C. `omega_(1) lt omega_(2)` when damping is small and `omega_(1) gt omega_(2)`
D. `omega_(1) = omega_(2)`

Answer

A

Explanation

`x_(0) = (F//m)/(sqrt((omega_(0)^(2) - omega^(2))^(2) + ((b omega)/(m))^(2)))` amplitude is maximum when
`omega_(1) = sqrt(omega_(0)^(2) - 2 gamma^(2))` and energy is maximum when `omega_(2) = omega_(0)`