Oscillations of Systems with Several Degrees of Freedom

In the first part of this chapter, we study oscillating systems with two (and subsequently with n) degrees of freedom. We learn the existence of particular motions, the normal modes, in which all parts of the system oscillate together harmonically. The number of modes, and the number of resonances, is equal to the number of degrees of freedom. We then study the modes of a vibrating sting. In the second part of the chapter, we study Fourier analysis, in regard to both periodic and non-periodic functions and for functions of both time and space.