## Engineering Mechanics: Statics & Dynamics (14th Edition)

$\omega_n=49.5 rad/s$;$T=0.127s$
We can determine the natural frequency and the period of vibration as follows: $K=\frac{mg}{\delta _{st}}$ $\implies K=\frac{3\times 9.81}{0.06}=490.5N/m$ Now the natural frequency is given as $\omega_n=\sqrt{\frac{K}{m}}$ We plug in the known values to obtain: $\implies \omega_n=\sqrt{\frac{490.5}{0.2}}=49.5rad/s$ and $T=\frac{2\pi}{\omega_n}$ We plug in the known values to obtain: $T=\frac{2\pi}{49.5}$ $\implies T=0.127s$