  In this paper we analyze the non-integrability of the Wilbeforce pendulum by
means of Morales-Ramis theory in where is enough to prove that the Galois group
of the variational equation is not virtually abelian. We obtain these
non-integrability results due to the algebrization of the variational equation
falls into a Heun differential equation with four singularities and then we
apply Kovacic's algorithm to determine its non-integrability.
