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QB3 (25 Marks) (a) Quantitatively describe the three (3) types of vibrations associated with the differential equation: 5f"(t) + f'(t) + 10f (t) = --2sin(t) (3) (3 Marks) (b). (. (0). Solve the differential equation: 5f"(t) + f'(t) + 10 (t) = 0,f(0) = 0; f'(0) = 4 (4) (ii). Determine the frequency and period of vibration; (iii) State the transient and steady state terms of the oscillation (iiv). Visualize the solution for t =(0:1:25) and comment on the observation. (9 Marks) (c). (i). (5) (ii). (iii). Solve the differential equation: f"(t) + f(t) = -2sin(t), f(0) = 0; f(0) = 1 Evaluate the frequency and period of vibration; Visualize the solution for t =(0:1:25) and comn (8 Marks) on observation. (d). What physical phenomena are represented by equations (4) and (5) and the corresponding solutions. Give two examples of Engineering Applications of each phenomenon observed. (5 Marks)