Q.Distinguish between free oscillations, damped oscillations and forced oscillations, giving one example of each.

A FREE oscillation occurs when a system is disturbed once and then left entirely alone, with no further external force acting and no energy lost to resistance; it oscillates at its own natural frequency $\omega_0$ (fixed by its own physical properties, e.g. $\sqrt{k/m}$ or $\sqrt{g/L}$), with an amplitude that ideally stays constant forever. Example: an idealised pendulum swinging in a vacuum after being released once.

A DAMPED oscillation occurs when the oscillating system continuously loses energy to a resistive force such as friction or air resistance; it still oscillates at very nearly its own natural frequency, but its amplitude steadily decreases with time until the motion eventually dies out. Example: a real pendulum swinging in air, whose swing visibly shrinks and eventually stops. …

Define each of the three terms in turn, stating what force (if any) acts and what happens to the amplitude and frequency in …

• Describing damped oscillation as though the frequency itself changes dramatically, when it is really the AMPLITUDE that changes, with the frequency staying very close to $\omega_0$ (for light damping). …