The electrical oscillations whose amplitude goes on decreasing with time are called damped oscillations.
The electrical oscillations whose amplitude remains constant with time are called undamped oscillations.

Damped and Undamped Oscillation

Damped Oscillation:
Damped oscillation refers to the motion of an oscillating system where the amplitude of the oscillations gradually decreases over time due to the presence of an external force or friction. This external force or frictional resistance acts against the motion of the system, resulting in the dissipation of energy and the gradual reduction of the amplitude of the oscillations.

Key Points:
- Damped oscillation occurs when there is a continuous loss of energy from the oscillating system.
- The energy loss is usually caused by factors such as friction, air resistance, or other forms of damping forces.
- The damping force opposes the motion of the system, leading to a decrease in the amplitude of the oscillations.
- The rate at which the amplitude decreases depends on the damping coefficient, which represents the strength of the damping force.
- In the case of heavy damping, the system eventually comes to rest without oscillating, as all the energy is dissipated.
- The motion of a damped oscillating system can be described by a differential equation that incorporates the damping term.

Undamped Oscillation:
Undamped oscillation, on the other hand, refers to the motion of an oscillating system where there is no dissipation of energy and the amplitude of the oscillations remains constant over time. In an undamped system, there are no external forces or frictional resistances acting against the motion, allowing the system to oscillate indefinitely without any loss of energy.

Key Points:
- Undamped oscillation occurs when there is no energy loss from the oscillating system.
- Without any damping forces, the system can continue oscillating indefinitely with a constant amplitude.
- The absence of external forces or frictional resistances allows the system to conserve its total energy.
- In an undamped system, the motion is characterized by the natural frequency of the system, which is determined by its mass and stiffness.
- The natural frequency represents the frequency at which the system would oscillate in the absence of any external influences.
- The motion of an undamped oscillating system can be described by a simple harmonic motion equation, which does not include any damping term.

In summary, damped oscillation refers to the gradual decrease in the amplitude of oscillations due to the presence of external forces or frictional resistances, while undamped oscillation refers to the motion of a system that does not experience any energy loss and maintains a constant amplitude over time.