A particle of mass (m) is attached to a spring (of spring constant k) and has a narural angular frequency omega_(0). An external force `R(t)` proportional to cos omegat(omega!=omega)(0) is applied to the oscillator. The time displacement of the oscillator will be proprtional to.

Options

A. `(m)/(omega_(0)^(2) - omega^(2))`
B. `(1)/(m(omega_(0)^(2) - omega^(2)))`
C. `(1)/(m(omega_(1)^(2) + omega^(2)))`
D. `(m)/(omega_(1)^(2) + omega^(2))`

Answer

B

Explanation

For forced oscillation,
`x = x_(0) sin (omega t + phi)` and `F = F_(0) cos omegat`
where `x_(0) = (F_(0))/(m(omega_(0)^(2) - omega^(2)) prop(1)/(m(omega_(0)^(2) - omega^(2))`