A particle \(P\) of mass \(m\) is attached to a light elastic string of natural length \(a\) and modulus \(mg\). The other end is fixed at \(O\) on a rough plane inclined at \(30^\circ\) to the horizontal. The particle is held at rest at \(O\) and released. The frictional force while it slides down the plane is \(\frac{11}{30}mg\).

(a) Find, in terms of \(a\), the distance moved down the plane before coming to rest.

(b) Given that \(P\) remains at rest in this new position, find the magnitude of the frictional force.