Driven Oscillator Quiz: Test Your Knowledge Of Forced Motion

The resonance curve shows how a driven oscillator responds differently at different driving frequencies, with a peak near the natural frequency.

Maximum steady amplitude occurs when the driving frequency matches the natural frequency, which is the resonance condition.

More damping increases energy loss per cycle, reducing maximum amplitude and widening the frequency range of noticeable response.

Bandwidth indicates how selective the oscillator is to frequency; narrow bandwidth means strong selectivity near resonance.

Low damping means energy stays stored in the oscillator for many cycles, producing a sharp peak with narrow bandwidth.

Higher Q means less energy lost per cycle relative to energy stored, corresponding to lower damping and a sharper resonance.

Energy transfer depends on the relative phase between force and velocity; near resonance, the timing aligns for efficient energy transfer.

Below resonance, the oscillator tends to follow the drive more closely; above resonance, it lags differently, with significant phase changes near the peak.

After driving begins, the system settles into steady-state determined mainly by the driving frequency and damping.

In steady-state, the driver supplies energy each cycle and damping removes it; amplitude stabilizes when these balance.

Low damping means slow energy loss, producing long-lasting oscillations after the driving force is removed.

Tuning forks vibrate for a long time and have a sharp frequency, while shock absorbers are designed to be heavily damped (low Q).

Natural frequency is determined by physical parameters; changing mass or stiffness changes the resonant frequency.

Resonance is general; any system that stores and exchanges energy between two forms can resonate.

Resonance produces a maximum response at a specific frequency, reflecting the system’s natural tendency to oscillate.

More damping removes energy faster, preventing the driver from building as large an amplitude before losses balance input.

A narrower bandwidth means greater selectivity and higher Q, linking Q to peak sharpness.

High damping dissipates energy and prevents large oscillations, improving ride comfort and safety.

Efficient timing allows energy to accumulate over many cycles; low damping prevents rapid loss, enabling large steady amplitudes from small inputs.

Resonance can be beneficial in instruments and filters but harmful to structures if uncontrolled; damping affects response size but doesn't need to be zero.