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_(0)^(2)+omega^(2)))`
D. `(m)/((omega_(0)^(2)-omega^(2)))`

Answer

B

Explanation

For forced oscillations `x = x_(0) sin (omegat +phi)` and `F = F_(0) cos (omegat)` where
`x_(0) =(F_(0)//m)/(sqrt((omega_(0)^(2)-omega^(2))^(2)+((bomega)/(m))^(2)))` here damping is zero `(b = 0)`