A system undergoes free oscillations when it is displaced from its equilibrium position and then left to vibrate under the action of its own restoring force alone, with no external driving force and no energy loss.
Every oscillating system has a characteristic natural frequency — the frequency at which it vibrates freely when disturbed. The natural frequency depends on the physical properties of the system:
For a simple pendulum: f=2π1lg — depends on length l and gravitational field strength g, not on the mass of the bob or the amplitude (for small angles).
For a mass–spring system: f=2π1mk — depends on spring constant k and mass m.
In an ideal (frictionless) free oscillation the amplitude and period remain constant indefinitely.
Forced oscillations occur when an external periodic driving force is continuously applied to an oscillator, compelling it to vibrate at the driving frequency rather than its own natural frequency.
The external force must continuously supply energy to counteract energy losses due to resistive forces (friction, air resistance) and maintain a steady amplitude.
If the driving frequency equals the natural frequency, resonance occurs and the amplitude becomes very large (see Topic 17.9).
Child on a swing — periodic pushes by an external agent supply energy at the driving frequency to maintain oscillation.
Pendulum of a clock — a small motor provides a periodic driving force to counteract energy losses and keep the pendulum swinging at a controlled frequency.
Loudspeaker cone — an alternating electrical signal drives the cone to oscillate at the signal frequency.
In any real oscillating system, resistive forces (friction, air resistance, viscous drag) oppose the motion and dissipate the system's mechanical energy — usually as heat. This causes the amplitude to decrease progressively over time. Such oscillations are called damped oscillations.
A damping force is a resistive force that opposes the velocity of the oscillator, causing it to lose energy and reducing its amplitude with each successive oscillation.