Pattern, scale, and a simple equation

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A periodic signal can be written compactly as $y(x) = A\sin(kx + \phi)$. The symbols hide a visual fact: amplitude, wavelength, and phase each change the pattern in a distinct way.

For a damped oscillation, one convenient form is

$$y(x) = A e^{-\gamma x}\cos(2\pi f x + \phi).$$

Equations are most useful here when they sharpen the prose, rather than replace it.