Please answer all parts of 14.12 (from Townsend Quantum Mechanics) below. Equations 4.34 and 4.44 are given below for reference.

14.12. A spin-} particle is immersed in a constant magnetic field Bo in the z direction and an oscillating magnetic field Bj cos cot in the x direction. The spin Hamiltonian can be written in the form H = woS, + wj cos wtS . See (4.34). Assume w|