Consider a SDOF system with $k=13,000\frac{N}{m},m=600kg$ and $=1\mathrm{.}0.$ Under an impulse

load, the maximum displacement was measured to be $0\mathrm{.}4$ m $.$ Determine the following:

$($a$)$ The damping constant $c.$

$($b$)$ The time it takes to reach the max displacement, and then the initial velocity.

$($c$)$ Plot the displacement vs$.$ time. Use MATLAB to plot.

$($d$)$ The time it takes for the mass to return to a position of $0\mathrm{.}01$ m from the initial position.

Note: $$

$(1)$ This is a problem of free vibration after impulse.

$(2)$ The velocity is zero when the displacement is maximum.