Answer
$k = 250~N/m$
Work Step by Step
We can find the effective spring constant of the musculature that holds the eyeball in its socket as:
$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$
$k = f^2~(2\pi)^2~m$
$k = (29~Hz)^2~(2\pi)^2~(0.0075~kg)$
$k = 250~N/m$
