What does it mean empirically if a bouncing ball's frequency depends on height? [closed]

What does it mean empirically if a bouncing ball's frequency depends on height?

That the trajectory's curvature will vary based on height?

I.e. we have a bouncing ball equation, where the ball's velocity

$$u_t=v$$, $$v$$ velocity

$$v_t =$$ function of height, e.g. $$-g-h^2$$, where $$g$$ is gravity.

The frequency is found by forming the Jacobian and solving the system's eigenvalues.

Since $$h$$ is retained in the Jacobian, then it's in the eigenvalues as well.

So we have eigenvalues:

$$\lambda = \pm i \sqrt{2} \sqrt{h}=\pm i\omega$$

and since $$\omega$$ is the frequency, then now it depends on $$h$$.

So the higher the $$h$$ the higher the frequency? But what kind of empirical sense does this make?

• it means the force pulling the ball back to the ground is not proportional to its height. can't imagine a situation where it would be. – Ben51 Feb 15 at 15:53
• Balls on springs. There you go – shai horowitz Feb 17 at 9:05