In: Mechanical Engineering
two subway cars as shown in Figure 1 have mass m = 2000 kg and are connected by a coupler that can be modeled as a spring of stiffness k = 280,000 N/m. Use Newton’s method to derive the equations of motion, calculate the natural frequencies and determine the associated mode shapes. also, find the time response x1(t) and x2(t) of the subway initial conditions: x(0)= [ 0, 0.2] with zero initial velocity vector.