Problem 2 An electric train pandograph in Fig. (1) is modelled as the 2-mass-spring lumped parameter model in Fig. (2). The model consists of the head mass m₁ = 2 kg and the frame mass m 2 = 5 kg. The shoe, head and frame stiffness coefficients are k₁ = 100 N/m, k₂ = 150 N/m and k 3 = 200 N/m, respectively. The input z(t) is a displacement input and the output of interest is the motion x(t) of the frame mass m 2. Displacements are measured from the equilibrium. a) Write the equations of motion that describe the system. b) Find the transfer function from the displacement input z(t) to the output x(t). Consider a sinusoid displacement input z(t) = 0.1 sin(wt) m. c) When the input frequency w = 8 rad/sec calculate the steady-state amplitude of the output motion x(t). d) What is the displacement transmissibility at this frequency w = 8 rad/sec? What is the steady-state amplitude of the force transmitted to the support roof wall W of the train due to the input excitation z(t)? e) Calculate the resonant frequencies of the system that result in unbounded amplitude for the output x(t). Fig. (1) k1 H m1 k2 k3 z (t) x(t) m2 Fig. (2) W