Q.1 A system has two blocks, A with a mass of 3 kg and B with a mass of 2 kg, as shown in Figure Q1. Mass A is connected

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Q 1 A System Has Two Blocks A With A Mass Of 3 Kg And B With A Mass Of 2 Kg As Shown In Figure Q1 Mass A Is Connected 1 (295.19 KiB) Viewed 38 times

Q.1 A system has two blocks, A with a mass of 3 kg and B with a mass of 2 kg, as shown in Figure Q1. Mass A is connected to a wall by a spring with a stiffness coefficient k = 5 N/m, while Mass B is connected to Mass A through a damper with a dampening coefficient c = 1 Ns/m. The system input is the forcing function FA(t) applied to Mass B, and the system output is the displacement of the mass A. +x1 +x2 с für А B FA FIGURE Q1 (a) Draw the free body diagram for each mass and derive the time-based ordinary differential equation of motion for each mass assuming linear relationships for the spring force, kx and damping force ci. (3 marks) (b) Using the following state variables, derive the state space representation of the system. 21 = x1,22 = x1 23 = x2,24 = x2 (5 marks) (c) Instead of using Hooke's law, if the spring force is given by the non-linear equation Fk = kx}, re-derive the equations of motion for both masses. (2 marks) = (d) Linearise the system in (c) around the point x1 = 1 m and derive the state space representation for this system, in the form: ż = AZ + B ) y = CZ + Du (10 marks)