We studied in class the phenomenon of resonance in forced, damped oscillators. The mass and stiffness of a one-dimensional oscillator give rise to a natural frequency of oscillations known as the resonance frequency. With no damping, energy input at this frequency accumulates and the amplitude of vibrations increases.
The phenomenon of resonance generalizes to linear elastic materials with many more (ie infinite) degrees of freedom: energy input at a natural frequency of vibration will accumulate and result in increasing amplitude of vibration. The natural frequency in this case is determined by material properties (ie Young's modulus) and the geometry and dimensions of the object (ie a wine glass). With so many degrees of freedom, the resonance frequency of common objects may be impossible to calculate exactly and it may be necessary to use the finite element method to investigate resonance.
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