Answer
$m=.06488 kg$
Work Step by Step
Simplifying the equation for frequency, we know:
$I=\frac{K}{4\pi^2f^2}$
Using the values of moments of inertias, we find:
$\frac{1}{2}Mr^2 + mr^2+mr^2 = \frac{K}{4\pi^2f^2}$
$\frac{1}{2}Mr^2 + 2mr^2 = \frac{K}{4\pi^2f^2}$
$ 2mr^2 = \frac{K}{4\pi^2f^2}-\frac{1}{2}Mr^2$
$m = \frac{\frac{K}{4\pi^2f^2}-\frac{1}{2}Mr^2}{2r^2 }$
$m = \frac{\frac{5}{4\pi^2(2.6)^2}-\frac{1}{2}(.34)(.25)^2}{2(.25)^2 }$
$m=.06488 kg$
