Wolfram Cloud Document

Clear["Global`*"];

ω=2000;

c1[ζ_]:=-ζω+ω

ζ

2

-1

;

c2[ζ_]:=-ζω-ω

ζ

2

-1

;

H[ζ_]:=

ω

2

(s-c1[ζ])(s-c2[ζ])

;

In[]:=

StepR[t_,ζ_]:=

ω

2

(c1[ζ]-c2[ζ])

*



c1[ζ]t

-1

c1[ζ]

-



c2[ζ]t

-1

c2[ζ]

(*UnitImpulseIntegratedbyhandUnitstepResponse*)

H1=

ω

2

(s+ω)

2

(*Transferfunctionwhenζ=1*)

(*RelevantTimeDomainFunctiont*

-ωt

*u(t)StepR1meanstheIntegralofitasbelow*)

StepR1[t_]:=ω

2

∫

t

0

τ*Exp[-ωτ]*UnitStep[τ]τ

In[]:=

Plot[{StepR[t,0.25],StepR[t,0.5],StepR[t,0.75],StepR1[t],StepR[t,1.5]},{t,0,0.010},PlotRangeAll,

PlotLegends"Expressions"]

In[]:=

0.002

0.004

0.006

0.008

0.010

0.5

1.0

1.5

	StepR(t,0.25)
	StepR(t,0.5)
	StepR(t,0.75)
	StepR1(t)
	StepR(t,1.5)

Out[]=

Manipulate[Control`PoleZeroPlot[{H[ζ]},PlotLabelStringForm["Pole Zero Plot for ζ = `1`",ζ],PlotLegends

StringForm["ζ = `1` ",ζ],PoleZeroMarkersStyle["x",Large,BackgroundCyan],AxesLabel{"Re","Im"}],{{ζ,

0.5},0,1}]

In[]:=

ζ

-1.0

-0.5

0.5

1.0

Re

-1.0

-0.5

0.5

1.0

Im

Pole Zero Plot for ζ = 0.5

ζ = 0.5

Out[]=