17.3 Damped and forced oscillations, resonance

A resistive force opposing motion transfers energy from an oscillating system to other stores, causing the amplitude to decrease with time.

The damping force may depend on speed; distinguish the ideal SHM frequency from the changed response of a damped system.

Air resistance makes a pendulum’s swings gradually smaller because mechanical energy becomes thermal energy in the air.

Damping does not necessarily stop oscillation immediately, and reduced amplitude is not the same as reduced equilibrium position.

Light damping allows oscillations with decreasing amplitude; critical damping returns to equilibrium fastest without oscillating; heavy damping returns more slowly without overshoot.

Sketch displacement against time with or without crossings of equilibrium and compare settling time, not just initial slope.

A door closer is designed near critical damping so the door settles promptly without repeated swinging.

Critical damping is not “maximum resistance” in every situation; too much damping can make return slower.

A driven oscillator resonates when the driving frequency is near a natural frequency, producing a large amplitude; damping limits and broadens the peak.

Identify the driving source, natural frequency and response amplitude. More damping usually lowers and broadens the resonance peak.

Pushing a swing at its natural period builds a larger motion than pushing randomly, even with the same average effort.

Resonance is not always destructive and does not require zero damping; it is a frequency-response phenomenon.