The system shown in Figure simulates a machine supported by rubbers, which are approximated as two identical spring-damper units. The input is the force f and the output is the displacement x of the mass. The parameter values are m = 500kg b = 250Ns / m and k = 400000N / m

k = 400N / m

1. Draw the necessary free-body diagram and derive the mathematical model of that machine.

2. Use MATLAB’s command to solve the differential equation

3. Use MATLAB’s command to plot the evolution of vibration of that mechanical engineering system for t in the interval [0,40]. When f = 5N

4. To evaluate the effect of the damping parameter b, Use MATLAB’s command to plot in the same graph the evolution of vibration when b = (0N / m) / s and b = (1.5N / m) / s

5. Analyze your result