Plot each image on the same figure. Use enough time increments so that the period of the largest frequency of oscillation has about 40 time increments per period

I have equations for y1(t) and y2(t) that i found from a two mass two spring system. I have solved these equations for 6 different sets of initial conditions, so now i have 6 equations for y1(t) and 6 equations for y2(t). I am extremely new to matlab, so I do not even know where to begin.

For each of the 6 sets of equations, i need to plot y1(t) and y2(t) on the same figure for efficient comparison.

I must use enough time increments so that the period of the largest frequency of oscillation has about 40 time increments per period and i must use a final time that is three times the smallest period.

Answer 1

[Ameer Hamza]

You can do something like this

t = 0:0.001:10;
y11 = 0.2763*cos(1.59*t) + 0.7237*cos(3.39t);
y12 = % 1st equation for y2
y21 = % 2nd equation for y1
y22 = % 2nd equation for y2
y31
..
..

and the plot like this

hold on % do draw all lines on same figure
plot(t, y11);
plot(t, y12);
plot(t, y21);
..
..

[Anna Zito]

Thank you that helps so much!! If I want to plot each set of initial conditions on a seperate graph (making 6 graphs in total; y11 & y12, y21 & y22, etc.) How would i do this? right now all lines for y11-y62 are on the same graph.

[Anna Zito]

I am also trying to plot y2(t)/y1(t) for each set on 6 graphs seperate from the first 6 mentioned above. This is the code that i came up with:

plot(t, y12/y11);

plot(t, y22/y21);

plot(t, y32/y31);

plot(t, y42/y41);

plot(t, y52/y51);

plot(t, y62/y61);

It is not displaying any figures. Why might this be?

[Image Analyst]

Did you overlook my answer below? It shows you how to get separate graphs (axes) using subplot. Then to plot the ratios, you'd simply call figure again and call subplot 6 more times.

[Anna Zito]

Oops! Sorry i did not realize that different axes meant separate graphs. That was very helpful!

My graphs are coming out very 'zig/zaggy' instead of a smooth sin/cosine curve. Do you have any idea why this might be?

[Image Analyst]

If you have enough points in there, like more than a thousand or so, then the usual cause is the renderer. What does this say

>> opengl info

You could try turning on or off "software" or change renderers. But I'm no opengl expert so you might just call the Mathworks tech support, or search this forum for renderer.

[Ameer Hamza]

For the issue related to plotting y2(t)/y1(t), you need to use element-wise operator

plot(t, y12./y11);
plot(t, y22./y21);
..

Answer 2

[Image Analyst]

For the same figure, different axes, use subplot

subplot(2, 3, 1);
plot(t, y1);
subplot(2, 3, 2);
plot(t, y2);
subplot(2, 3, 3);
plot(t, y3);
subplot(2, 3, 4);
plot(t, y4);
subplot(2, 3, 5);
plot(t, y5);
subplot(2, 3, 6);
plot(t, y6);

For the same axes, use hold on:

plot(t, y1);
hold on;
plot(t, y2);
plot(t, y3);
plot(t, y4);
plot(t, y5);
plot(t, y6);

To find the period, realize that the number 1.59 or 3.39 is 2*pi/period. So

period1 = 2 * pi / 3.39
period2 = 2 * pi / 1.59
shortestPeriod = min([period1, period2]);
finalTime = 3 * shortestPeriod;
numSamples = % I'm sure you can figure this out.
t = linspace(0, finalTime, numSamples);