Damping: (i) the effects of damping on an oscillatory system

The idea

Damping removes energy from an oscillatory system, so the amplitude of free oscillations decreases over time. Light damping gives a gradual decay with the period almost unchanged; heavy damping returns the system to equilibrium slowly without oscillation; critical damping returns it in the shortest time without overshoot. The energy lost per cycle depends on the damping, and the decay envelope of a lightly damped system falls exponentially.

For example: A pendulum in air loses a small fraction of its energy each swing, so its amplitude shrinks slowly while its period stays close to the undamped value.

What earns the marks

• Damping is the removal of energy from an oscillatory system, usually transferred to thermal stores, so the amplitude of free oscillations decreases with time.
• Light damping produces a gradual exponential decay of amplitude while the period remains approximately constant.
• Heavy damping causes the system to return to equilibrium slowly, without completing oscillations.
• Critical damping returns the system to its equilibrium position in the shortest time without overshoot, and is the boundary between oscillatory and non-oscillatory behaviour.
• The rate of energy loss per cycle increases with the degree of damping, so the amplitude decay is faster for heavier damping.

Common mistakes and how to put them right

• Believing that damping changes the period of a lightly damped oscillator appreciably.

  Put it right: For light damping the period is almost unchanged; the main observable effect is the decaying amplitude.

• Confusing heavy damping with critical damping.

  Put it right: Heavy damping returns the system to equilibrium slowly, while critical damping returns it in the shortest time without overshoot.

• Thinking that damping adds energy to the system.

  Put it right: Damping removes energy, typically transferring it to thermal stores, which is why the amplitude falls.

• Assuming a damped system stops oscillating immediately.

  Put it right: Light damping allows many oscillations with gradually decreasing amplitude.

Exam tips

• Sketch the displacement–time graph for light, heavy and critical damping side by side so you can recognise and describe each case quickly.
• When explaining energy loss, state where the energy goes, for example to thermal stores, rather than saying it simply disappears.
• Use the phrase 'amplitude decreases exponentially' for light damping and reserve 'no overshoot' for critical damping to keep descriptions precise.