Answer
$x=0.167cos 6.55t$
Work Step by Step
We can determine the required equation as follows:
$x=\frac{v_{\circ}}{\omega_n} sin(\omega_nt)+x_{\circ} cos(\omega_n t)$eq(1)
As $\omega_n=\sqrt{\frac{K_{eq}}{m_{eq}}}$
$\implies \omega_n=\sqrt{\frac{20/3}{5/32.2}}=6.552rad/s$
We plug in the known values in eq(1) to obtain:
$x=0+\frac{2in}{12in/ft}cos(6.552t)$
$\implies x=\frac{1}{6}cos(6.552t)$
$\implies x=0.167cos 6.55t$
