Q.What are undamped oscillations?

When a circuit oscillates, the behaviour of its amplitude over time decides whether the oscillations are damped or undamped, while the frequency stays the same in both cases.

Damped oscillations are oscillations whose amplitude keeps decreasing with time and finally falls to zero. This happens whenever the circuit loses more energy each cycle than is returned to it — for example, a real LC tank loses energy in the coil's resistance, in radiation, and in the capacitor's dielectric, so each successive swing is smaller than the last and the waveform decays inside a shrinking envelope.

Undamped (sustained) oscillations are oscillations whose amplitude remains constant with time. Here the energy lost per cycle is exactly replaced from an external source, so every swing is the same size and the output continues indefinitely. A practical oscillator must deliver undamped oscillations, so the whole design goal is to keep the amplitude from decaying — usually by adding an amplifier that feeds back just enough energy each cycle. …