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What does the equation $\frac{d^2 y}{d t^2}=-k y$, with $k>0$ represent?
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The equation
$\frac{d^2 y}{d t^2}=-k y \text {, with } k>0$
represents what happens when an object is subject to a force towards an equilibrium position with the magnitude of the force being proportional to the distance from equilibrium.

The above equation can be considered as an approximation to the equation of motion of a particular point on the basilar membrane, or anywhere else along the chain of transmission between the outside air and the cochlea.
by Platinum (141,884 points)

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