Consider a constant magnetic field B0 = 1.5 T is applied to an object. The gyromagnetic ratio of the object is γ = 2π × 4, 258 (rad/s)/G. Suppose the following RF pulse is applied
where 
f = 4.258 × 104 Hz, A = 2 G/Hz, τp = 2 ms, and ν0 is the Larmor frequency.
(a) Find ν0. Write down an equation to calculate the tip angle.
(b) Assume τp is long enough so that B1(t) could be approximated as
What is the spectrum of B1(t)? Sketch it. Suppose a slice selection gradient is applied in z direction while B1(t) is applied and Gz = 2 G/cm.
(c) Where is this slice centered? What is the slice thickness?
(d) If you want to select another slice adjacent to the current slice (moving in the +z direction) with the same slice thickness, how should you change the RF pulse? Assume Gz stays the same.
(e) Right after the RF pulse in (d), what is the maximum phase difference of the spins inside the current slice? How does one rephase the spins?
(f) Suppose you want to sample k-space using a sampling trajectory that starts as shown in Figure P13.10. Assume that |Gx| = 2.5 G/cm and |Gy| = 1.5 G/cm. Sketch a pulse sequence to achieve this part of the trajectory. Indicate the acquired signal, the readout gradient, the phase-encoding gradient, and the slice selection gradient.
(g) For the sampling indicated in (e), if FOVx must be 50 cm, what is the smallest sampling rate fs?
