Asked to plot using vectors of unequal sizes

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B.M.
B.M. 2014-2-9
评论： B.M. 2014-2-10
I am working on the following problem:
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We wish to examine the motion of a damped harmonic oscillator. The small amplitude oscillation of a unit mass attached to a spring is given by the formula y = e−(R/2)t sin(ω1t ), where ω2 1 = ω2 o − R2/4 is the square of the natural frequency of the oscillation with damping (i.e., with resistance to motion); ω2 o = k is the square of the natural frequency of undamped oscillation; k is the spring constant; and R is the damping coefficient. Consider k = 1 and vary R from 0 to 2 in increments of 0.5. Plot y versus t for t from 0 to 10 in increments of 0.1.
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My main problem with this problem is that I am told to evaluate y for R=0:0.5:2, but plot over the range of t=0:0.1:10. How can this work, if y is 1x5 and t is 1x101?
Here is my code, minus the line for t, which I make the same as R to get y, but then try to change when going to plot (doesn't work):
========================================
k= 1; %spring constant
R=[0:0.5:2]; %damping coeff
w0=sqrt(k);
w1=sqrt((w0^2)-R.^2/4);
y=exp(-(R./2).*t).*(sin(w1.*t));
plot(t,y)

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Mischa Kim
Mischa Kim 2014-2-10
编辑：Mischa Kim 2014-2-10
B.M., simply compute y in a for-loop and plot the results in the same figure using hold all. You also might want to include markers and a legend for readability. Use colors and markers to specify the color and marker type for each of the plots.
k = 1; %spring constant
R = 0:0.5:2; %damping coeff
t = 0:0.1:10;
w0 = sqrt(k);
w1 = sqrt((w0^2)-R.^2/4);
figure
hold all; grid; box
colors = 'krbcy';
markers = 'x+*.o';
for ii = 1:length(R)
y(ii,:) = exp(-(R(ii)/2).*t).*(sin(w1(ii)*t));
plot(t,y(ii,:),[markers(ii) colors(ii)]);
end
xlabel('t in s')
ylabel('y in TBD')
legend('R0','R1','R2','R3','R4')
  1 个评论
B.M.
B.M. 2014-2-10
Thanks Mischa. The book I'm using hasn't gone into much detail about plotting yet so I figured there was some more complicated way to do it...just wish I could figure out what they were expecting given the simple discussion so far.

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