$[$Ch$5-3]$ Determine the vibration response of an underdamped system to a constant force that is applied for a short period of time $(t_1=2sec)$ and then removed $($see figure$)$

$cdots{F}_0=30N,k=1000\frac{N}{m}$

$=0\mathrm{.}1$ and ${}_n=3\mathrm{.}16ra\frac{d}{s}$

$x(t)=\frac{F_0}{k}-\frac{F_0}{k\sqrt[\phantom{2}]{1-{}^2}}{e}^{-{}_n(t-t_0)}cos[{}_d(t-t_0)-],t{t}_0$

where $,=ta{n}^{-1}(\frac{}{\sqrt[\phantom{2}]{1-{}^2}})$

Note that the system is underdamped