Question

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball 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 that holds the eyeball in the socket?

Short answer

The effective sprint constant is 248.757 N/m

Step-by-step solution

Introduction

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

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

where

f$f=29Hz$Hz is the frequency of oscillation

$\mathrm{m}=7.5\mathrm{g}=0.0075\mathrm{kg}$is the mass of the eyeball

k is the spring constant

Solving equation for $k$

$$\begin{gathered} k={\left(2\times \pi \times 29\right)}^2\times 0.0075 \\ k={(2\times 3.14\times 29)}^2\times 0.0075k=248.757N/m \end{gathered}$$