A mass, spring and a damper system is subjected to an external harmonic excitation of $200$ cos $5$ t $($ N $).$ Find the response for the following givens: $K=4000\frac{N}{m},m=10kg,c=40N\frac{s}{m},x_0=0\mathrm{.}1m$ and $v_0=10\frac{m}{s}$

Select one:

$e^{\mathrm{.}01127}(-0\mathrm{.}005sin0\mathrm{.}9595t-0\mathrm{.}0345cos0\mathrm{.}9595t)+0\mathrm{.}0347sin(5t-3\mathrm{.}058)$

$0\mathrm{.}45e^{-27}cos(21\mathrm{.}899t+0\mathrm{.}02671)+0\mathrm{.}066cos(20t-0\mathrm{.}1325)$

$0\mathrm{.}4958e^{2t}cos(19\mathrm{.}899t+1\mathrm{.}4383)+0\mathrm{.}066cos(5t*0\mathrm{.}1325)$

$0\mathrm{.}0345e^{77}cos(19\mathrm{.}899t+0\mathrm{.}02671)+0\mathrm{.}066cos(5t-0\mathrm{.}1325)$