The amplitude become large when the frequency of the driving force $(\omega )$ is near the natural frequency of oscillation or when $\omega ={\omega }_0$. This frequency is known as resonance frequency. Amplitude of oscillation for a forced, damped oscillator is 

$A=\frac{f_{0/m}}{\sqrt{({\omega }^2-{\omega }_0^2)+(b\omega /m{)}^2}}$
where $b$ is constant related to the strength of the resistive force, ${\omega }_0=\sqrt{k/m}$ is natural frequency of undamped oscillator $(b=0)$.