Answer
$y=-0.05cos (20t)$
Work Step by Step
We can determine the required equation as follows:
We know that
$y=\frac{v_{\circ}}{\omega_n}sin\omega_n t+y_{\circ}cos\omega_n t~~~~eq(1)$
As $\omega_n=\sqrt{\frac{K}{m}}$
$\implies \omega=\sqrt{\frac{800}{2}}=20rad/s$
Now, we plug in the known values into equation (1) to obtain:
$y=\frac{0}{20}sin20 t-0.05 cos 20t$
$\implies y=-0.05cos (20t)$
