ABSTRACT
In Chapter 3, we investigated few-degree-of-freedommechanical and electrical systems that exhibit
simple harmonic oscillation about a stable equilibrium state. In this chapter, we shall extend this
investigation to deal with many-degree-of-freedom mechanical systems, made up of a number of
identical coupled single-degree-of-freedom systems, that likewise exhibit simple harmonic oscil-
lation about a stable equilibrium state. We shall find that, in the limit as the number of degrees
of freedom tends to infinity, such systems morph into physically continuous, uniform, mechanical
systems that exhibit standing wave oscillations. A standing wave is a disturbance in a physically
continuous mechanical system that is periodic in space as well as in time, but which does not propa-
gate; that is, both the nodes, where the amplitude of the oscillation is zero, and the anti-nodes, where
the amplitude of the oscillation is maximal, are stationary. In this chapter, we shall restrict our in-
vestigation to transverse waves; that is, waves in which the direction of oscillation is perpendicular
to the direction along which the phase of the waves varies sinusoidally.
