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
For `x = x_(0) sin (omega + t theta) & F = F_(0) cos omega t`
Where `x_(0) = (F_(0)/(m))/sqrt((omega_(0)^(2)-omega^(2)) + ((b omega)/(m))^(2))`
here b = 0