Physics · Ch 10 — Oscillations
Damped oscillations
Damped oscillations
The free-oscillation picture assumes no energy loss, but real oscillators sit inside a real medium -- air, oil, or some structural material -- whose friction and drag continually remove energy from the motion. As a result the amplitude of oscillation steadily decreases with time even though the oscillation frequency stays close to the natural frequency; the particle still oscillates sinusoidally, but its amplitude decays within an exponentially-shrinking 'envelope'. This behaviour, in which the oscillator loses energy that is absorbed by the surrounding resistive medium, is called damped oscillation. The resistive (damping) force responsible is proportional to the velocity of the oscillator, always opposing its motion. Examples: a pendulum swinging in air or immersed in an oil-filled container, the electromagneti …
What this figure shows. A displacement-versus-time curve shows an oscillator that still swings sinusoidally between positive and negative displacement, but whose peak-to-peak swing keeps shrinking as time goes on, so that the whole sinusoidal wiggle is bounded above and below by a pair of smooth, symmetric, exponentially-decaying dashed curves forming an 'envelope' that pinches in towards zero displacement as t increases. This is the signature graphical shape of damped oscillation: the same underlying frequency as the undamped case, but with an amplitude that dies away smoothly rat …