Figure 4 shows a solid rectangular bar of length L, mass m and moment of inertia I = ml. The bar is connected to a sprin

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Figure 4 Shows A Solid Rectangular Bar Of Length L Mass M And Moment Of Inertia I Ml The Bar Is Connected To A Sprin 1 (89.89 KiB) Viewed 10 times

Figure 4 shows a solid rectangular bar of length L, mass m and moment of inertia I = ml. The bar is connected to a spring of stiffness k and a damper with coefficient of damping c. Assume the bar oscillates through frictionless bearings at 'O' and that m= 1kg, c = 3 Ns/m and k = 4 N/m. The lengths L1, L2 and L are given in the caption to Figure 4. = [4 marks] (a) Draw a free body diagram of this system for the case that the bar is displaced by a small amount 8(0) radians and released from rest and derive the equations of motion. (b) Determine the natural frequency wn and damping ratio 6. (c) Find the particular solution for the case (0) = 0.2 m and ò(0) = 0 m/s. (d) Explain, very briefly, the meaning of critical damping. What value of corre- sponds critical damping? [3 marks] [11 marks] [2 marks] or с m 4 L2 L Figure 4: This Figure refers to Q4. Assume L1 = 0.5, L2 = 0.75 and L = 1 m.