Manipulate[
Module[{sol},
sol=u/.First@NDSolve[{(m/32)u''[t]+(1/4)u'[t]+16u[t]==4Cos[2t],u[0]==0,u'[0]==0},u,{t,0,20}];
Plot[sol[t],{t,0,20},PlotRange->{-1,1}]
],
{{m,8,"weight"},.1,200,Appearance->"Labeled"}
]