Forced Oscillations and Resonance

Abstract

In this chapter, we study a mechanical system forced to oscillate by the application of an external force varying harmonically with time. The amplitude of the oscillations, which is shown to depend on the frequency of the external force, reaches its peak value when the frequency of the applied force is close to the natural frequency of the system, a phenomena called resonance. However, details depend on the energy loss in the system, a property described by a quality factor Q, and the phase difference is described by so-called phasors. Emphasis is placed on how the system behaves when the external force starts and vanishes. Numerical calculations facilitate the analysis. At the end, some relevant details concerning the physiology of the human ear are briefly mentioned.