Answer
$14rad/s$
Work Step by Step
We can find the required angular velocity as follows:
$K=\frac{mg}{\delta}$
$\implies K=\frac{25\times 9.81}{0.05}=4905N/m$
Now $\omega=\sqrt{\frac{K}{m}}$
We plug in the known values to obtain:
$\implies \omega_n=\sqrt{\frac{4905}{25}}$
$\implies \omega_n=14rad/s$
