Answer
The frequency of oscillation is $91~Hz$
Work Step by Step
When the web is displaced a distance $d = 0.030~mm$, the upward force by the web is equal in magnitude to the fly's weight. We can find an expression for the spring constant $k$:
$kd = mg$
$k = \frac{mg}{d}$
We can find the frequency of oscillation:
$f = \frac{\omega}{2\pi}$
$f = \frac{1}{2\pi}~\sqrt{\frac{k}{m}}$
$f = \frac{1}{2\pi}~\sqrt{\frac{mg}{md}}$
$f = \frac{1}{2\pi}~\sqrt{\frac{g}{d}}$
$f = \frac{1}{2\pi}~\sqrt{\frac{9.80~m/s^2}{0.030\times 10^{-3}~m}}$
$f = 91~Hz$
The frequency of oscillation is $91~Hz$
