2: Oscillations: Plots:

Clear["Global`*"]

Manipulate[Plot[Sin[x(1+a x+b (x^2))],{x,0,6}],{{a,1},0,2},{{b,1},0,2}]

eq1=x''[t]+2β x'[t]+w0^2 x[t] == q0 Exp[I wD t]

initial={x[0]==x0,x'[0]==v0};

eq2= Join[{eq1},initial]

dsol=DSolve[ eq2,x,t][[1]]

values={β->0.1, w0->1, wD ->3,x0->1,v0->1,q0->1};
x[t] /.dsol //.values

Plot[x[t] /.dsol //.values //Re,{t,0,50}]

Clear[term]
term[w0_,wD_,β_,x0_,v0_,q0_][t_] =x[t] /.dsol  //Re;
term[1.,2,3,4,5,6][1.1]

Manipulate[
Plot[term[w0,wD,β,x0,v0,q0][t],{t,1,40},PlotRange->All, AspectRatio->1/3,ImageSize->Large],
{{w0,1},1,7,1},
{{wD,3},1,7,1},
{{β,0.1},0,5,0.1},
{{x0,1},-1,1},
{{v0,1},-5,5},
{{q0,1},0,5.0}
]