Dangerous Amplitude

A rigid cylindrical body of mass $m = 250 \text{kg}$ is resting over a soil layer having coefficient of uniform elastic compression $= 200 \text{kN/m}^3$ as shown in figure:

If the body is subjected to a excitation of $20 \sin(10 t) \text{kN}$ in horizontal direction and a vertical moment of $60 \sin(10 t) \text{kNm}$ . Then determine the amplitude of motion along horizontal displacement $A_x$ (in $\text{m}$ ) and rotational amplitude $A_{\theta}$ (in $\text{rad}$ ).

Find $\large \frac{A_x}{A_{\theta}}$ .