4. [25 pts] The Lagrangian for a system of one degree of freedom can be written as L= ½m(q² sin² wt+qqwsin2wt + q²w²) . (a) [5 pts] Find the equations of motion by using Lagrange's equation and interpret the equations by giving a physical interpretation of the forces acting on the particle. (c) [10 pts] Find the canonical momentum and construct the Hamiltonian. Is this Hamiltonian a constant of the motion? (d) [10 pts] Introduce a new coordinate defined by Q = qsinwt. Find the Lagrangian in terms of the new coordinate and the corresponding Hamiltonian. Is this new Hamiltonian a constant of the motion?