In free underdamped oscillation, the amplitude refers to the maximum displacement or maximum distance that an oscillating object moves from its equilibrium position during one complete cycle of oscillation.
In the case of underdamped oscillation, the amplitude of the oscillating system gradually decreases over time due to the presence of damping. The rate at which the amplitude decreases depends on the damping factor of the system.
Initially, when the oscillation begins, the amplitude is at its maximum. As time progresses, the amplitude gradually decreases until it reaches zero, at which point the oscillations cease.
In summary, the amplitude in free underdamped oscillation refers to the maximum displacement from the equilibrium position during one complete cycle of oscillation, and it decreases over time due to damping.