Physics - 1 - 50 - Harmonics

Author:Feynman
Language: eng
Format: epub
Tags: Physics, Feynman, Waves, Harmonics

0) LINEAR

(b) NONLINEAR

Fig. 50-4. Linear and nonlinear responses.

50-6 Nonlinear responses

Finally, in the theory of harmonics there is an important phenomenon which should be remarked upon because of its practical importance—that of nonlinear effects. In all the systems that we have been considering so far, we have supposed that everything was linear, that the responses to forces, say the displacements or the accelerations, were always proportional to the forces. Or that the currents in the circuits were proportional to the voltages, and so on. We now wish to consider cases where there is not a strict proportionality. We think, at the moment, of some device in which the response, which we will call ;c out at the time /, is determined by the input x m at the time t. For example, * in might be the force and x oui might be the displacement. Or x [n might be the current and x out the voltage. If the device is linear, we would have

*out(0 = Kx in (t\

(50.24)

where K is a constant independent of / and of X[ n . Suppose, however, that the device is nearly, but not exactly, linear, so that we can write

*Ml1

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