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Problem on displacement response time history

(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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