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\( \DeclareMathOperator{\abs}{abs} \)
(%i12)
laplace
(
3
,
t
,
s
)
;
\[\mathrm{\tt (\%o12) }\quad \frac{3}{s}\]
-->
(%i13)
ilt
(
%
,
s
,
t
)
;
\[\mathrm{\tt (\%o13) }\quad 3\]
(%i1)
exp
(
-
6
*
t
)
*
sin
(
4
*
t
)
+
exp
(
-
6
*
t
)
*
cos
(
4
*
t
)
;
\[\mathrm{\tt (\%o1) }\quad {{e}^{-6\cdot t}}\cdot \mathrm{sin}\left( 4\cdot t\right) +{{e}^{-6\cdot t}}\cdot \mathrm{cos}\left( 4\cdot t\right) \]
(%i2)
laplace
(
%
,
t
,
s
)
;
\[\mathrm{\tt (\%o2) }\quad \frac{6+s}{{{s}^{2}}+12\cdot s+52}+\frac{4}{{{s}^{2}}+12\cdot s+52}\]
(%i3)
ratsimp
(
%
)
;
\[\mathrm{\tt (\%o3) }\quad \frac{10+s}{{{s}^{2}}+12\cdot s+52} = \frac{s + 10}{(s+6)^2 + 16}\] Siste formen er på mathlabplus sin foretrukne form.
(%i2)
( (
54
/
s
^
4
)
-
(
12
/
s
^
3
)
+
(
4
/
s
^
2
) )
;
ilt
(
%
,
s
,
t
)
;
\[\mathrm{\tt (\%o1) }\quad \frac{4}{{{s}^{2}}}-\frac{12}{{{s}^{3}}}+\frac{54}{{{s}^{4}}}\]\[\mathrm{\tt (\%o2) }\quad 9\cdot {{t}^{3}}-6\cdot {{t}^{2}}+4\cdot t\]
Inverse laplace:
Find the inverse Laplace transform of: \[\mathrm{}\quad \frac{s + 10}{(s+6)^2 + 16}\]
(%i1)
ilt
(((
s
+
10
)
/
expand
(((
s
+
6
)
^
2
)
+
16
)),
s
,
t
)
;
\[\mathrm{\tt (\%o1) }\quad {{e}^{-6\cdot t}}\cdot \left( \mathrm{sin}\left( 4\cdot t\right) +\mathrm{cos}\left( 4\cdot t\right) \right) \] \[\mathrm{}\quad \mathcal{L}^{-1} \{\frac{s + 10}{(s+6)^2 + 16}\} = \mathcal{e}^{-6t}\mathrm{sin}\ 4t+\mathcal{e}^{-6t}+\mathrm{cos}\ 4t\]
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wxMaxima
.
