Consider a Lagrangian of the form
L=21m(x˙2−ω2x2)eγt,
where the particle of mass m moves in one direction. Assume all constants are positive.
(a) Find the equations of motion.
(b) Interpret the equations by giving a physical interpretation of the forces acting on the particle.
(c) Find the canonical momentum and construct the Hamiltonian. Is this Hamiltonian a constant of the motion?
(d) If initially x(0)=0 and dx/dt=0, what is x(t) as t approaches large values?