Phys I--Mechanics:  Resonance

Define a dimensionless frequency ration ωr  = ωd/ω0.  Also define a dimensionless amplitude:  (A/((F0/(((mω0)^2)))). Q is the “quality factor”, namely √(k m) / b.

A[ωr_, Q_] := ((1/(ωr))/(Sqrt[((((1/(ωr))- ωr))^2)+ (1/(Q^2))]))

Manipulate[Plot[A[ωr, Q], {ωr, 0.01, 2.0}, PlotRange->{0, 20}, PlotLabel ->Q,
LabelStyle->Larger, AxesLabel -> {"frequency", "Amplitude"}, ImageSize -> Scaled[0.8]], {{Q, 5}, 0, 20, 0.25,Appearance -> "Open"}, ControlPlacement -> Top]

Qs = Table[Q, {Q, 13, 1, -2}];
fig = Plot[Evaluate[Table[A[ωr,Q], {Q, Qs}]],{ωr, 0.01, 2.0}, 
PlotLabel-> "Resonance",
FrameLabel -> {"frequency/natural frequency", "Amplitude"}, PlotRange->All, LabelStyle->Larger, PlotLegends -> Qs,  Frame -> True, ImageSize -> Scaled[0.8]]

Export["Ch14-resonance-fig-1.pdf", fig]