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