Marion Problem 3.24

Ac=-1;ω0=1;β=0.2;ω1=(Sqrt[((ω0)^2)-(β^2)]);
δ=ArcTan[((ω0)^2)-(((α*ω1))^2),2*α*ω1*β];
xc[t_,Ac_,β_,ω1_]=Ac*(E^(-β t))*Cos[ω1*t];
xp[t_,Ap_,β_,ω1_,ω0_,δ_,α_]=(Ap/(Sqrt[(((((ω0)^2)-(((α*ω1))^2)))^2)+4*(((α*ω1))^2)*(β^2)]))*Cos[α*ω1*t-δ];
x[t_,Ac_,Ap_,β_,ω1_,ω0_,δ_,α_]=xc[t,Ac,β,ω1]+xp[t,Ap,β,ω1,ω0,δ,α];
Manipulate[
GraphicsGrid[
{
{Plot[
{xc[t,Ac,β,ω1],xp[t,Ap,β,ω1,ω0,δ,α]},{t,0,b},
PlotRange->{{0,b},{-a,a}},
AxesLabel->{"t","x"},
PlotStyle->{{Dashed,Thick,Red},{Thick,Blue}},
ImageSize->600
]
},
{Plot[
x[t,Ac,Ap,β,ω1,ω0,δ,α],{t,0,b},
PlotRange->{{0,b},{-a,a}},
AxesLabel->{"t","x"},
PlotStyle->{Thick,Orange},
ImageSize->600
]
}
}
],
{{α,(1/9),"(ω/(Subscript[ω, 1]))"},{(1/9),(1/3),1.1,3,6},Setter},
Delimiter,
{{Ap,1,"(Subscript[A, p])"},{1,20},Setter},
Delimiter,
{{a,1.6,"(Subscript[x, max])"},0.1,3,0.1,Appearance->"Labeled"},
{{b,30,"(Subscript[t, max])"},10,100,5,Appearance->"Labeled"},
ControlPlacement->Right
]