Hand written solution required

Advanced Physics Consider a simple pendulum of mass m and length L, in which the point under the support oscillates horizontally according to the equation x = a coswt], as shown the image below: a) Write the appropriate general coordinates. b} Find the Lagrangian Land Lagrange equation{s}. c) Show that the Lagrangian above can be rewritten as follows: " d L = L + 33}, being fa function that depends only on generalized coordinates andfor time. Get the new one{s} Lagrange equation(s] and compare with those obtained from item b. d} Obtain the Hamiltonian of the system. is the Hamiltonian a constant of motion? Does the Hamiltonian correspond to the energy of the system