How do I plot a Laplace transform?

Question

I have been looking everywhere for help on this issue and cannot find a solution that works. Here is the assignment.

I have figured out how to find the Laplace transform, but I do not know how to graph it. Here is my code:

de1 = 25 x''[t] + 10 x'[t] + 226 x[t] == 901*Cos[3 t];
inits = {x[0] -> 0, x'[0] -> 0};
DE = LaplaceTransform[de1, t, s]
X = Solve[DE, LaplaceTransform[x[t], t, s]]
X = X // Last // Last // Last
X = X /. inits
f1 = InverseLaplaceTransform[X, s, t] // Expand

And here is the resulting inverse Laplace transform, or the solution (I think):

(-(1/2) - (451 I)/30) E^((-(1/5) - 3 I) t) - 
  (1/2 - (451 I)/30) E^((-(1/5) + 3 I) t) + Cos[3 t] + 30 Sin[3 t]

But how do I graph it?

Answer 1

Copying your exact code

de1 = 25*Derivative[2][x][t] + 10*Derivative[1][x][t] + 226*x[t] == 901*Cos[3*t]; 

inits = {x[0] -> 0, Derivative[1][x][0] -> 0}; 

DE = LaplaceTransform[de1, t, s]

X = Solve[DE, LaplaceTransform[x[t], t, s]]

X = Last[Last[Last[X]]]

X = X /. inits

f1 = Simplify[Expand[InverseLaplaceTransform[X, s, t]]]

Now it's easy to plot as range from 0

Plot[f1, {t, 0, 40}]