4. For a system of single particle in one-dimension, the Lagrangian is given as (m2 kq2) mg L = evt 2 2 Where y, m, and k are the system parameters. = (malo - a) Determine the Lagrangian equation of motion. b) For the Lagrangian given in Problem, derive the expression for the Hamiltonian and the Hamiltonian equation of motion. c) Verify if energy is conserved for the Hamiltonian obtained in