QUESTION 2 The forced oscillations of a body of mass m on a spring of modulusk (as shown in Figure 2) are governed by th

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Question 2 The Forced Oscillations Of A Body Of Mass M On A Spring Of Modulusk As Shown In Figure 2 Are Governed By Th 1 (30.01 KiB) Viewed 35 times

QUESTION 2 The forced oscillations of a body of mass m on a spring of modulusk (as shown in Figure 2) are governed by the ODE: my" + cy' + ky = r(t) where y = y(t) is the displacement from rest. c is the damping constant, k is the spring constant (spring modulus), and r(t) is the external force depending on time, t. с Spring m Ball Extemal force r(t Dashpot Figure 2: Vibrating system (a) Let m = 1 gm, c = 0.05 gms and k = 25 gms-2 Write the ODE of the system. (1 mark) (b) Given the external force r(t) (measured in gmcm s-4): t+<t<0 r(t) = TT t + TT - + 0 <t< r(t + 2) = r(t). Plot the external force r(t). Then, determine the Fourier Series of r(t). (5 marks) (c) Based on (a) and (b), find the steady-state solution y(t) by showing that 4(25 – nº) 0.2 A= B = -; D. = (25-n") + (0.05n)2 n2D TLD (3 marks) (d) Plot the steady-state solution y(t). (1 mark)