ABSTRACT
Before we can continue to the propagation of sound waves, we have to treat the principles of free and forced vibrations.
Consider an object of a mass m attached by a massless elastic spring to a motionless ceiling at rest, as displayed in Figure 3.1. Let us dene this equilibrium position as x = 0. The mass is pulled back over a distance x by a force F . For a stationary mass,
F = sx; (3.1)
where s is the stiness of the spring. The elastic potential energy gained equals the work done by stretching the elastic object:
EP =
F dx =
s x dx =
2 s x2
= 1
2 sx2: (3.2)
After release, we can dene the excursion x(t) around the equilibrium by
m x = s x (3.3) or
a = s m
x: (3.4)
Using
a = dv
=
dv
dx
= v
dv
; (3.5)
Figure 3.1: Massm on a spring with stiness s, pulled back by a distance x.
