In forced vibration, the amplitude of the oscillations may increase, decrease, or remain constant depending on the system's characteristics and the nature of the forcing function.

1. Amplitude Increase:

If the frequency of the external driving force is close to the system's natural frequency, resonance occurs. At resonance, the amplitude of the oscillations increases significantly. This phenomenon is characterized by a sharp increase in the system's response to the driving force.

2. Amplitude Decrease:

Conversely, if the driving force's frequency is significantly different from the natural frequency, the amplitude of oscillations may decrease. This phenomenon is called detuning. Detuning occurs when the system's natural frequency is either much lower or much higher than the driving force's frequency.

3. Constant Amplitude:

In certain situations, the amplitude may remain constant over time. This happens when the system is sufficiently damped, or the damping forces are strong enough to counteract the energy input from the external driving force.

Therefore, whether the amplitude decreases or not in forced vibration depends on the system's natural frequency, the driving force's frequency, and the damping present in the system.