How do I plot a Laplace transform?

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?

• Your link shows that this is a homework assignment. This is not a site for us to do your homework assignments. (Vote to close.) – David G. Stork Mar 21 at 18:27
• what's you range for plotting on both axes !? – Alrubaie Mar 21 at 18:48
• If you can't figure out your homework you can always ask the stack exchange, vote to close :( – olliepower Mar 21 at 18:50
• It's not that I don't know how to do my homework, I just needed help with the Mathematica/coding portion of it. – Stephanie Green Mar 21 at 19:19
• @StephanieGreen For what it's worth, I agree: yours was not a "gimme da codez" kind of question. You included your code attempts and showed effort. I hope that this community's initial response did not alienate you, and I am looking forward to further contributions from you! – MarcoB Mar 21 at 20:55

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}]


• Awesome, thank you so much! – Stephanie Green Mar 21 at 19:18