Problem on displacement response time history

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(i) Formulate the equation of motion for the system shown in Figure below. List two assumptions made in this formulation.

(ii) Find the response of this system at t = 3s. The system begins with the displacement of 5 cm and velocity of 3 cm/s. Given that m = 300 kg, k = 5 kN/m and c = 150 Ns/m. Draw the displacement response time history.

1596_displacement response.jpg

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