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
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?