$19\mathrm{.}21$ and $19\mathrm{.}22$ A $50-$kg block is supported by the spring arrangement

shown. The block is moved vertically downward from its equilibrium

position and released. Knowing that the amplitude of the resulting

motion is $60$ mm $,$ determine $($a$)$ the period and frequency of the motion,

$($b$)$ the maximum velocity and maximum acceleration of the block.

Fig. P$19\mathrm{.}21$

Fig. P $19\mathrm{.}22$

If a vertical force of P$=30$ sin $($wt$)($N$)$ is applied to the mass spring system in P$19\mathrm{.}21,$ determine the forcing frequencies w if the magnitude of the steady state response is $10$ mm

If a vertical force of P$=5$ sin $(17$t$)($N$)$ is applied to the mass spring system in P$19\mathrm{.}22$ determine the magnification factor and the amplitude of the steady state response