
209Harmonic Oscillator
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This integral (Equation 7.28) is the area in the phase space (p, q); J is known as an action variable
in classical mechanics.
7.3 DAMPED HARMONIC OSCILLATOR
Free oscillation is an ideal physical case. In practice, dissipative forces are always present in any
system. A simple example of the damped oscillator is the free motion of a particle of mass m
attached to a (massless) spring in a resisting medium as shown in Figure 7.8. Let x be the displace-
ment of m from position A at which point the spring is unstretched (of length a). The restoring force
is –kx. We now limit ourselves to the case ...