In this problem, we answer the question: What is the tip angle that maximizes MR signal intensity for a pulse sequence with given TR and TE values? Solve this problem for given T₁, T₂, and T∗ 2 values. Assume that the magnetization is in the steady-state condition, that is, the magnetization is a periodic function of time with a period of T_R. Also assume that the transverse magnetization completely dephases before each RF pulse, that is, M_xy(0⁻) = 0.

(a) Calculate M_Z(0⁻), the steady-state magnetization value just before the R_F pulses.

(b) Calculate M_xy(T_E), the signal level in the steady-state condition.

(c) Calculate the optimum tip angle.