A First-order Model-A Hydraulic Clutc

Given in Figure is the iconic model of a hydraulic clutch undergoing tests. In this setting, a motor drives the left disk of the clutch at a controlled rate omega(t) while the right disk is coupled to a linearly elastic shaft of torsional stiffness k and negligible inertia. Moreover, the right end of the shaft is clamped to a fixed wall.

1. Derive the Lagrangian of the system.

2. Derive the mathematical model of the device

3. GIVE the inputs and outputs

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

5. Use MATLAB’s command to plot the evolution with time t. M = 50kg C = 25Ns / m and k = 40N / m

6. Use MATLAB’s command to plot in the same grap the evolution with time t when C = 0 and when C = 10 N-s/m. Analyse.