Question

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball held by the musculature in its socket.
If the mass of the eyeball is 7.5 g, a typical value, what is the effective spring constant of the musculature attached to the eyeball

Answer 1

The effective spring constant of the system is 39.6 N/m

Explanation:

The frequency of oscillation of a spring-mass system is given by

$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

where

k is the spring constant of the system

m is the mass

In this problem, we have:

f = 29 Hz is the frequency of vibration of the eyeball system

m = 7.5 g = 0.0075 kg is the mass

We can therefore re-arrange the equation to find the effective spring constant of the system. We find:

$k=(2\pi f)^2 m = (2\pi (29))^2 (0.0075)=39.6 N/m$

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