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 \(\large \frac{A_x}{A_{\theta}}\).

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