In[]:=
Clear["Global`*"];ω=2000;c1[ζ_]:=-ζω+ω-1;c2[ζ_]:=-ζω-ω-1;H[ζ_]:=;
2
ζ
2
ζ
2
ω
(s-c1[ζ])(s-c2[ζ])
StepR[t_,ζ_]:=*-1--1(*UnitImpulseIntegratedbyhandUnitstepResponse*)
2
ω
(c1[ζ]-c2[ζ])
c1[ζ]t
c1[ζ]
c2[ζ]t
c2[ζ]
H1=(*Transferfunctionwhenζ=1*)(*RelevantTimeDomainFunctiont**u(t)StepR1meanstheIntegralofitasbelow*)
2
ω
2
(s+ω)
-ωt
In[]:=
StepR1[t_]:=τ*Exp[-ωτ]*UnitStep[τ]τ
2
ω
t
∫
0
In[]:=
Plot[{StepR[t,0.25],StepR[t,0.5],StepR[t,0.75],StepR1[t],StepR[t,1.5]},{t,0,0.010},PlotRangeAll,PlotLegends"Expressions"]
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In[]:=
Manipulate[Control`PoleZeroPlot[{H[ζ]},PlotLabelStringForm["Pole Zero Plot for ζ = `1`",ζ],PlotLegendsStringForm["ζ = `1` ",ζ],PoleZeroMarkersStyle["x",Large,BackgroundCyan],AxesLabel{"Re","Im"}],{{ζ,0.5},0,1}]
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