Resonance

At resonance, there is maximum transfer of energy between the hand and the mass-spring system. Plotting amplitude

with respect to

, shows a curve that is almost symmetrical about its peak $A_{max}$ , i.e., it has a bandwidth measured a distance down from $A_{max}$ .

**Figure 9:** A Resonator shows peak amplitude when the driving force is equal to the system's natural frequency.
$\scalebox{0.4}{\includegraphics{eps/resonator.eps}}$

Both the peak $A_{max}$ the bandwidth $\Delta f$ depend on the damping in the system:

heavily damped: $\Delta f$ is large and $A_{max}$ is small.
little damping: $\Delta f$ is small and $A_{max}$ is large, creating a sharp resonance.

``MUS 206: Mechanical Vibration'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).