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

δ[ω_,Q_] := Piecewise[{
{ArcTan[(ω/(Q (1 - (ω^2))))],ω < 1},
{(π/2),ω == 1},
{ ArcTan[(ω/(Q (1 - (ω^2))))] + π,ω > 1}
}]

Manipulate[
{Plot[A[ω,Q],
{ω,0,2},
AxesLabel -> {"ω/(Subscript[ω, 0])","A/((Subscript[F, 0])/k)"},
PlotRange -> {0,20},
PlotLabel -> "Amplitude",
PlotStyle -> {Blue,Thick},
ImageSize -> {500,300}
],
Plot[
δ[ω,Q],
{ω,0,2},
AxesLabel -> {"ω/(Subscript[ω, 0])","δ"},
PlotRange -> {0,π},
PlotLabel -> "Phase Difference",
PlotStyle -> {Green,Thick},
Exclusions->None,
ImageSize -> {500,300}
]},
{{Q,1,Dynamic["Quality Factor Q"]},0.1,20,Appearance -> "Labeled"}
]