Q.Explain in detail the four different types of oscillations.

Step 1. Free oscillations. An oscillator displaced and released, with no further outside influence, vibrates at its own natural frequency; in the idealised (frictionless) case, amplitude, frequency and total energy all stay constant. Examples: a struck tuning fork, a plucked string, an idealised frictionless pendulum or spring-mass system.

Step 2. Damped oscillations. Real oscillators lose energy to friction and drag in the surrounding medium, so their amplitude steadily decreases with time within an exponentially decaying envelope, even though the frequency stays close to the natural frequency; the damping force is proportional to velocity. Examples: a pendulum in air or oil, an LC tank circuit's dying oscillations, dead-beat/ballistic galvanometers.

Step 3. Maintained oscillations. To prevent this decay, energy is supplied from an external source, exactly enough each cycle to replace what damping removes, keeping the amplitude constant indefinitely while the oscillator still vibrates near its own natural frequency. Example: a pendulum clock's escapement mechanism.

Step 4. Forced oscillations. An oscillator driven by an external periodic force initially responds partly at its own natural frequency, but this transient dies away, and the system settles into steady vibration at the driving frequency instead. Example: a stringed instrument's sound board, forced to vibrate at the frequency of the plucked strings. …

Work through each of the four types in turn -- free, damped, maintained, forced -- defining each by its energy behaviour, and close with reso …

• Treating maintained and forced oscillations as the same thing; maintained oscillation stays at the natural frequency with just-replaced energy, while forced oscillation settles at the driving frequency. …