In Chapter 3, we investigated few-degree-of-freedom mechanical 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 oscillation 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 propagate; 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 investigation 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.
