The fixed points \(A\) and \(B\) are on a smooth horizontal surface with \(A B=2.6 \mathrm{~m}\). One end of a light elastic spring, of natural length 1.25 m and modulus of elasticity \(\lambda \mathrm{N}\), is attached to \(A\). The other end is attached to a particle \(P\) of mass 0.4 kg . One end of a second light elastic spring, of natural length 1.0 m and modulus of elasticity \(0.6 \lambda \mathrm{~N}\), is attached to \(B\); its other end is attached to \(P\). The system is in equilibrium with \(P\) on the surface at the point \(E\).
(i) Show that \(A E=1.4 \mathrm{~m}\).

The particle \(P\) is now displaced slightly from \(E\), along the line \(A B\).
(ii) Show that, in the subsequent motion, \(P\) performs simple harmonic motion.

(iii) Given that the period of the motion is \(\frac{1}{7} \pi \mathrm{~s}\), find the value of \(\lambda\).