Problem 3.5 Show that fright = x' cos 2wt + y' sin 2wt (3.43) using steps like those used in deriving (3.21). Its time average is clearly zero. 0 = -WE (3.16) The unit vector a' rotates clockwise, with time, in the negative o direction. i' = i coswt - y sinwt = R=(wt)i (3.17) assuming a'(0) = (0). Similarly, y' = a sin wt + y coswt = R= (wt)y (3.18) The B, field can be expressed in terms of the primed basis. The inversion of (3.17) and (3.18) is i = a' cos wt + y' sin wt = R.(-wt)i' (3.19) y = -i' sin wt + i' coswt = R.(-wt)y' (3.20) equivalent, as noted, to the rotation of the primed unit vectors by R,(-wt) in the positive o-direction. From double-angle trigonometric formulas, (3.15) and (3.19) lead to Blin = - blin [a'(1 + cos 2wt) + y'sin 2wt] (3.21)Problem 26.7 Sampling artifacts can manifest themselves in subtle ways. Two examples are considered in this problem. The issues of aliasing have already been addressed in earlier chapters. What effect would you expect to see in the image if a) The sampling accuracy was not perfect and a small jitter in sampling time occurred about each point? b) A remnant time-dependent magnetic field gradient in the readout direction of the form G..e "t/ is present during sampling where 7., is on the order of T