Please solve part d,e,f A simple pendulum of mass m and length L is shown in the figure below. Take the reference of potential energy at the lowest point of pendulum. L h PE = 0 a) Determine the number of constraints. ( b) Show that the degree of freedom is equal to 1 c) Choose the angle 0 as generalized coordinate to determine the expressions of the kinetic energy and the potential energy. (. d) Write down the expression of Lagrangian L. e) Find the expression of generalized momenta P f) Write down the expression of Hamiltonian as a function of Pom, L, 0 and gravity g. g) Determine the equation of motion

Please solve part d,e,f A simple pendulum of mass m and length L is shown in the figure below. Take the reference of potential energy at the lowest point of pendulum. L h PE = 0 a) Determine the number of constraints. ( b) Show that the degree of freedom is equal to 1 c) Choose the angle 0 as generalized coordinate to determine the expressions of the kinetic energy and the potential energy. (. d) Write down the expression of Lagrangian L. e) Find the expression of generalized momenta P f) Write down the expression of Hamiltonian as a function of Pom, L, 0 and gravity g. g) Determine the equation of motion