(* Oops!  It turns out that I didn't need the Block[] command that I used in the first version of this file.  The semicolons between expressions are sufficient to create a "compound statement." *)
ClearAll["Global`*"];
Manipulate[
soln = NDSolveValue[{x''[t] + 2 beta x'[t] + omega0^2 x[t] == 0, x'[0]==v0, x[0]==x0}, x[t], {t, 0, tmax}];
Plot[soln, {t, 0, tmax}, PlotRange->All],
{{omega0, 1.0}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{beta, 0.1}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{x0, 1.0}, 0, 5.0, Appearance -> "Labeled", LabelStyle->Large},
{{v0, 0.0}, 0.0, 10.0, Appearance -> "Labeled", LabelStyle->Large},
{{tmax, 30}, 0, 100, Appearance -> "Labeled", LabelStyle->Large}, LabelStyle->Large]

ClearAll["Global`*"];
Manipulate[ 
beta = omega0 / (2 Q);
soln = NDSolveValue[{x''[t] + 2 beta x'[t] + omega0^2 x[t] == 0, x'[0]==v0, x[0]==x0}, x[t], {t, 0, tmax}];
Plot[soln, {t, 0, tmax}, PlotRange->All],
{{omega0, 1.0}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{Q, 0.5}, 0.01, 100.0, Appearance -> "Labeled", LabelStyle->Large},
{{x0, 1.0}, 0, 5.0, Appearance -> "Labeled", LabelStyle->Large},
{{v0, 0.0}, 0.0, 10.0, Appearance -> "Labeled", LabelStyle->Large},
{{tmax, 30}, 0, 100, Appearance -> "Labeled", LabelStyle->Large}, LabelStyle->Large]

ClearAll["Global`*"];
omega0 = 1.0;
Manipulate[
soln = NDSolveValue[{x''[t] + 2 beta x'[t] + omega0^2 x[t] == fampl Cos[omega t+fphi], x'[0]==v0, x[0]==x0}, x[t], {t, 0, tmax}];
Show[
Plot[{soln,fampl Cos[omega t + fphi]}, {t, 0, tmax}, PlotRange->All]],
{{omega, 1.0}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{beta, 0.1}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{fampl, 1.0}, 0, 2.0, Appearance -> "Labeled", LabelStyle->Large},
{{fphi, 0.0}, -Pi, Pi, Appearance -> "Labeled", LabelStyle->Large},
{{x0, 0.0}, -5.0, 5.0, Appearance -> "Labeled", LabelStyle->Large},
{{v0, 0.0}, 0.0, 10.0, Appearance -> "Labeled", LabelStyle->Large},
{{tmax, 100}, 0, 1000, Appearance -> "Labeled", LabelStyle->Large}, LabelStyle->Large]