solution=DSolve[{y''[x]+2*g*y'[x]+w^2*y[x]==0,y[0]==50,y'[0]==0},y[x],x][[1,1,2]]

Manipulate[Plot[solution/.g->gamma/.w->omegazero,{x,-10,10}, PlotRange->All],{gamma,0,10},{omegazero,1,20}]