Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about thi...
Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about this axis. [5 marks] x (t) k2 b) Then use Lagrange's Equation to determine the equations of motion. M(t) denotes an external moment applied to the cylinder. Also, express the equations in matrix form. [10 marks] c) Comment briefly on the dominant dynamic effects you would expect to see if Jis very large in comparison with m and M(t) is a small sinusoidal torque of frequency a. mar
Question 5 (20 marks) a) Develop a Lagrangian for the system shown, for small displacements from equilibrium when 6 (t)-0. The cylinder rotates on a fixed axis and has moment of inertia, J, about this axis. [5 marks] x (t) k2 b) Then use Lagrange's Equation to determine the equations of motion. M(t) denotes an external moment applied to the cylinder. Also, express the equations in matrix form. [10 marks] c) Comment briefly on the dominant dynamic effects you would expect to see if Jis very large in comparison with m and M(t) is a small sinusoidal torque of frequency a. mar