A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ${\mathrm{\omega }}_0$. An extemal force F(t) proportional to $\cos \mathrm{\omega } \mathrm{t}(\mathrm{\omega } \ne {\mathrm{w}}_0)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

• A

  $\frac{\mathrm{m}}{{\displaystyle {\mathrm{\omega }}_0^2-{\mathrm{\omega }}^2}}$

• B

  $\frac{1}{\mathrm{m}\left({\displaystyle {{\displaystyle \mathrm{\omega }}}_0^2}{\displaystyle -}{\displaystyle {{\displaystyle \mathrm{\omega }}}^2}\right)}$

• C

  $\frac{1}{\mathrm{m}\left({\displaystyle {{\displaystyle \mathrm{\omega }}}_1^2}{\displaystyle +}{\displaystyle {{\displaystyle \mathrm{\omega }}}^2}\right)}$

• D

  $\frac{\mathrm{m}}{{\displaystyle {\mathrm{\omega }}_1^2+{\mathrm{\omega }}^2}}$