# How can I plot a result of Laplace Transform? [duplicate]

Is it possible to Plot the output of LaplaceTransform with Mathematica?

Obviously when I apply LaplaceTransform to a function I obtain a function of parameter s... but is implicit defined as sigma+j*omega, but I can't see this....(like the following example shown).

LaplaceTransform[Sin[t], t, s]

1/(1 + s^2)


Can I plot this function? Can I plot the Abs[] of the Laplace transformed function?

I wish obtain a graphic like this

Thx :)

• @Artes I don't see the Re+Im part, because appear only parameter " s " , so i think that my question isn't a duplicate – plus91 May 16 '17 at 12:00
• Plot3D[Abs[1/(1 + s^2) /. s -> x + I y], {x, -2, 2}, {y, -2, 2}, PlotRange -> {0, 2}] – Artes May 16 '17 at 12:01
• @Artes thx, now it's clear :D – plus91 May 16 '17 at 12:21

The answer is YES, it is possible to Plot the output of LaplaceTransform with Mathematica.

To understand how to plot functions in general read the documentation for Plot.

Plot[
1/(1 + s^2)
, {s, -4, 4}
]


Your would get the same if you use

Plot[
Evaluate@LaplaceTransform[Sin[t], t, s]
, {s, -4, 4}
]


or if you assign a new function name to the the transformed function

out[s_] = LaplaceTransform[Sin[t], t, s]

Plot[
out[s]
, {s, -4, 4}
]


For complex s you could use

Plot3D[
Abs[1/(1 + Complex[x, y]^2)]
, {x, -1, 1}
, {y, -1, 1}
, MaxRecursion -> 5
]


Or

Plot3D[
Evaluate@ReIm[1/(1 + Complex[x, y]^2)]
, {x, -1, 1}
, {y, 0, 2}
, MaxRecursion -> 5
, PlotStyle -> {
Directive[Red, Opacity[0.3]]
, Directive[Blue, Opacity[0.3]]
}
]