Question

(15 points) This problem is related to Problem 3.7 in the text. consider reviewing Section 3.2.1.1. The following MATLAB program plots the function v(t) = 5 cos(300 - 24t) + 2 sin (600 - 2x + ) t = 0: step :Tmax; V = 5* cos(2pi"300"t) + 2 sin(2"pi*600*t + pi/2); plot(t,v) xlabel('time (seconds)') ylabel('signal v(t)) axis([xmin,xmax,ymin,ymax]) What is the period of the signal v(t)? Suppose that we want to produce a plot that covers exactly 4 periods and has exactly 20 samples per period. Determine the appropriate values of step Tmax Determine the values of xmin, xmax, ymin, and ymax to give a good visual plot and avoid the function hitting the boundaries of the plot. help [xmin, xmax] = (numbers) ſymin, ymax) = { help (numbers) If you do not get the correct answer in 3 tries, you may access hints below.

Answer 1

The first term of the function has period 1/300s

The second term of the function has period 1/600s

So the time period of the function v(t) is LCM(1/300,1/600) = 1/300 s = Tperiod

4 periods = 4/300 s = Tmax

step = 1/20 * 1/300 s (To get 20 samples per period)

xmin = -Tperiod (Since the function starts at 0)

xmax = Tmax + Tperiod (Since the function ends at Tmax)

min(v(t)) = -5-2 = -7

max(v(t) = 5+2 = 7

ymin = min(v(t)) - 1 = -8

ymax = max(v(t)) + 1 = 8

-------------------------------------------Code------------------------------------------------

Tmax = 4/300;
step = 1/20 * 1/300;
xmin = -1/300;
xmax = Tmax + 1/300;
ymin = -8;
ymax = 8;

t = 0:step:Tmax;
v = 5*cos(2*pi*300*t) + 2*sin(2*pi*600*t + pi/2);
plot(t,v)
xlabel('time (seconds)')
ylabel('signal v(t)')
axis([xmin,xmax,ymin,ymax])

Tmax = 4/300; step = 1/20 * 1/300; xmin = -1/300; xmax = Tmax + 1/300; ymin = -8; ymax = 8; ороо со мол во ме IIIIIIIIIIII t = 0:step: Tmax; v = 5*COS (2*pi*300*t) + 2*sin (2*pi*600*t + pi/2); plot(t,v) xlabel('time (seconds)') ylabel('signal v(t)') axis ( [xmin, xmax, ymin, ymax])

signal v(t) 10 5 time (seconds) *10-3