Hand written solution required

Two Lagrangians L(q, q, t) and L'(q, q, t) differ by the total time derivative of some function o(g,() ['(q. 4, t) = L(9. 9.t ) + do a) Show that they describe the same one degree of freedom physical system, i.e., they give the same equation of motion. b) What is the relation between the generalized momenta p' and p which these two Lagrangians yield? c) What is the relation between the Hamiltonians H' and H which these two Lagrangians yield? d) Show explicitly that Hamilton's equations for both Hamiltonians are equivalent