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L me X4 m3, J3 ks ke O kz: m2 Y.1 λ = = = m, kg = 7x10' N/m, ka = 7.5x10' N/m, kz = kg = 3x10 N/m, kg = 5x104 N/m, m = m2 = 20 kg, m3 = 250 kg, m4 = 80 kg, Jz = 190 kg.m’, L = 0.75 m, i = 6 m, x = 3 cm, v=110 km/h = In the figure, a simplified model of the wheels-body-seat system of a vehicle moving in a sinusoidal path is shown. a) Obtain the differential equations for the small amplitude vibrations of the system. b) Determine the mass and stiffness matrices of the system. c) Using the given numerical values, find the natural frequencies and mode shapes of the system and the forced vibration amplitudes.