f[x_]:=(x^3)(((x-π))^3)

Plot[f[x],{x,0,π}]

g[x_?Positive]:=f[x];
g[x_?Negative]:=-f[-x];
g[0]=0;
h[x_]:=g[x-2π Floor[((x+π)/(2π))]]

Plot[g[x],{x,-π,π}]

Animate[Plot[(1/2)(h[x+t]+h[x-t]),{x,0,π},PlotRange->{-16,16}],{t,0,2π,.1}]