transform my function into the laplace domain in matlab

To transform a function f(t) into the Laplace domain in Matlab, you can use the Symbolic Math Toolbox. Here's an example of how to do it:

main.m
syms t s
f = cos(2*t) - 3*exp(-4*t); % define the function
F = laplace(f); % transform into the Laplace domain
F = simplify(F) % simplify the result
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In this example, f(t) = cos(2t) - 3e^(-4t) is defined as a symbolic expression using the syms command. The Laplace transform of f is then obtained using the laplace function. Finally, the result is simplified using the simplify function.

You can substitute specific values for s to obtain the Laplace transform at specific points in the complex plane. For example:

main.m
F1 = subs(F, s, 1+i); % substitute s=1+i
F2 = subs(F, s, 2); % substitute s=2
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This will give you the Laplace transform of f at s=1+i and s=2, respectively.