Finding inverse Laplace when the inverse Laplace function is a piecewise function

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Aleem Andrew
Aleem Andrew 2021-3-4
回答： Walter Roberson 2021-3-5
I wrote the following Matlab program to find x in the time domain.
syms y(t) m k x c w F s
eqn = s^2*x-s+2*s*x-2+2*x == exp(-pi*s);
x = ilaplace(solve(eqn,x),s); x = simplify(x)
The output is
x =
exp(-s)*(cos(s) + sin(s) - exp(pi)*sin(s)*heaviside(s - pi))
Matlab failed to find the inverse Laplace in the time domain because x(t) is a piecewise function. Can someone explain how the correct value of x in the time domain can be found?

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Walter Roberson
Walter Roberson 2021-3-5
rewrite(x, 'piecewise')

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