In[]:=
a=2*Pi*5*^3;ac=2*Pi*1;​​lap=a/(p^2+a^2)*(1-e^(-0.001*p))*(p^2+a^2)/(p^2+p*ac+a^2)//Together​​lapZahler=Numerator[lap]​​lapNenner=Denominator[lap]​​(PolStellen=Solve[lapNenner0,p])//TableForm​​PolStelle1=p/.PolStellen[[1]]​​PolStelle2=p/.PolStellen[[2]]​​lap1=Apart[lapZahler/((p-PolStelle1)*(p-PolStelle2)),p]​​ua[t_]:=InverseLaplaceTransform[lap1,p,t]​​Plot[ua[t],{t,0,2*^-3},AxesOrigin{0,0},GridLinesAutomatic,GridLinesStyleDirective[Orange,Dashed],PlotLabel"",AxesLabel{},PlotStyle{Thin,Blue}]​​ua[t]
Out[]=
10000
-0.001p
e
(-1+
0.001p
e
)π
2
p
+2pπ+100000000
2
π
Out[]=
10000(-1+
0.001p
e
)π
Out[]=
0.001p
e
(
2
p
+2pπ+100000000
2
π
)
Out[]//TableForm=
p-3.14159-31415.9
p-3.14159+31415.9
Out[]=
-3.14159-31415.9
Out[]=
-3.14159+31415.9
Out[]=
-
(0.+0.159155)((-3.14159+0.)+(3.14159+0.)
0.001p
e
)
(3.14159-31415.9)+1.p
+
(0.+0.159155)((-3.14159+0.)+(3.14159+0.)
0.001p
e
)
(3.14159+31415.9)+1.p
Out[]=
Out[]=
InverseLaplaceTransform-
(0.+0.159155)((-3.14159+0.)+(3.14159+0.)
0.001p
e
)
(3.14159-31415.9)+1.p
+
(0.+0.159155)((-3.14159+0.)+(3.14159+0.)
0.001p
e
)
(3.14159+31415.9)+1.p
,p,t