Use the following hints: HW Problem 3 (Hints) ____________ (i) Property "x(t) = 2.4 for 18% of each period" is preserved when shifting or scaling occurs on the horizontal axis - i.e., property is unaffected by the values of W (Omega) and q (phi). Take W = 1 and q = 0 for simplicity, and note that in each cycle, the section above a certain level is symmetric about the peak. ANS: A = 2.4/cos(9*pi/50). (ii) It takes 0.123 seconds for the angle (phase) of the cosine to change from 9*pi/50 (where A*cos(9*pi/50) = 2.4) to pi (where A*cos(pi) = -A = minimum) ANS: W = 2*pi/0.3 = 20*pi/3 rad/sec (iii) t = 0 occurs 0.040 seconds before a zero. Use W (rad/sec) to convert this amount of time to an angle. A zero occurs at two phase values within [0,2*pi) - what are they? ANS: q = 7*pi/30 rad or q = 37*pi/30 rad (same as -23*pi/30 rad) (iv) The two versions of x(t) corresponding to the two values of q differ in algebraic sign only, so abs(x(t)) will be the same for both. d = 1/150; % fraction of period between samples t = (0 : d : 2-d)*0.3; % time grid (etc.)

Use your calculator for algebraic caleulations only. Solutions based on trial and error, inspection of numerical plots, ete., are not acceptable. Consider the sinusoid x(t) = Acos(Qt+@), where A 0 and (z, 7]. Time is in seconds. It is known that e x(t) 2.4 for exactly 18% of each period; * it takes 0.123 seconds for the value of the sinusoid to drop from 2.4 to the next minimum (\"valley\"); * the first zero of the sinusoid in positive time occurs at = 0.040 (seconds). (i) (5 pts.) Determine the amplitude A. (ii) (5 pts.) Determine the period and angular frequency Q of s(t). (iii) (5 pts.) Determine the initial phase @ of x(t) as a fraction of +. (Two values are possible here.) (iv) (5 pts.) Write simple MATLAB code which computes and plots two periods of |x(t)| (ie., the absolute value of (f)) starting at = 0, using 150 uniformly spaced samples per period (i.e., a total of 300 samples). Attach a printout of the code and a plot of the result