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Laplace using Matlab

Laplace using Matlab - by hand in the lecture notes>>...

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Laplace Transforms and Inverse Laplace Transforms Using Matlab Matlab has the ability of finding the transforms using the laplace (*) and ilaplace (*) functions. First: Any symbolic variables need to be defined using the syms . laplace() will look for the varialbe t and return the transform in s. Here are two examples below: >> syms b t >> laplace(t^3) ans = 6/s^4 >> laplace(exp(-b*t)) ans = 1/(s+b) Matlab can return the inverse Laplace transform using ilaplace(). Ilaplace() will look for a variable s and return the transform in t. Here is the example we did
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Unformatted text preview: by hand in the lecture notes. . >> syms b s >> ilaplace(s/((s+1)*(s^2+2*s+5))) ans = -1/4*exp(-t)+1/4*exp(-t)*cos(2*t)+1/2*exp(-t)*sin(2*t) You can see that f(t) is not identical as the one we did in class, but using simple trig identities, we can make it look identical. That is not really a concern. What is useful is observing the plot of >> t1 = 0:.01:10; >> f = -1/4*exp(-t1)+1/4*exp(-t1).*cos(2*t1)+1/2*exp(-t1).*sin(2*t1); >> plot(f) Here we see that the system returns to a relaxed state in about 6 seconds....
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