(* Set the values of the various parameters *)
mu=0.05;
a = 1.0;
w0 = 1;

(* Solve the differential equations with the given set of initial conditions. *)
sol = NDSolve[
{x'[t] == v[t],
v'[t] == -mu*(x[t]*x[t] - a*a)*v[t] - w0*w0*x[t],
x[0] == 1,
v[0] == 0},
{x,v},{t,0,50*2*Pi},MaxSteps -> 20000];

(* Plot the solution of the differential equations *)
ParametricPlot[Evaluate[{x[t],v[t]} /. sol],{t, 0, 50*2*Pi}, 
PlotRange->All,
AxesLabel -> {"x (rad)","v (rad/s)"}]