Question

Why the amplitude is small in forced vibration?

Answer 1

Only when the frequency of the driving force is not in sync with the natural frequency of the oscillator.

Explanation:

If the driving frequency does not in sync with the natural frequency, then the energy can not be absorbed to increase the amplitude. In fact, it can impede the motion. Think about a swing. If you don't hit the rope of the swing at the right frequency (natural frequency of the swing), instead of help pushing it higher, you are likely to mess up the swing.

The amplitude can increase greatly if the driving frequency is matching the natural frequency.