(1) What is the resonance condition? (5 points) (2) Prove the following relationship (15 points): R(a)...

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(1) What is the resonance condition? (5 points) (2) Prove the following relationship (15 points): R(a) = R(-a) = R(a) (3) Calculate and sketch B,rot (t) assuming that (25 points) B(t) = B cos(wrft +/4)i- B sin(wst+/4)] (4) Assume that a spin system with a single resonance component was at thermal equilibrium. Calculate the transverse magnetization resulting from the following excitation sequences (20 points): (a) 90%, followed by 90% (b) 45% followed by 90% (1) What is the resonance condition? (5 points) (2) Prove the following relationship (15 points): R(a) = R(-a) = R(a) (3) Calculate and sketch B,rot (t) assuming that (25 points) B(t) = B cos(wrft +/4)i- B sin(wst+/4)] (4) Assume that a spin system with a single resonance component was at thermal equilibrium. Calculate the transverse magnetization resulting from the following excitation sequences (20 points): (a) 90%, followed by 90% (b) 45% followed by 90%