Hand written solution required

A transformation in phase space is given as Q =aq + Ap P =aq - 3p where a and / are constants. a) For which values of n and / is this transformation a canonical one? b) Find the generating function of type one, Fi(q. Q). c) Apply this transformation with a = - to the one-dimensional harmonic oscillator whose hamilto- nian is given as H = ( p3 + 97 ) to find the new Hamiltonian. d) Obtain the Hamilton's equations of motion for the new Hamiltonian and solve them. Hamiltonian expression shoul not contain any velocity term