2 A particle of mass \(m\) is attached to the mid-point of a light elastic string. The string is stretched between two points \(A\) and \(B\) on a smooth horizontal surface, where \(A B = 2 a\). The string has modulus of elasticity \(\lambda\) and natural length \(2 l\), where \(l < a\). The particle is in motion on the surface along a line passing through the mid-point of \(A B\) and perpendicular to \(A B\). When the displacement of the particle from \(A B\) is \(x\), the tension in the string is \(T\). Given that \(x\) is small enough for \(x ^ { 2 }\) to be neglected, show that $$T = \frac { \lambda } { l } ( a - l )$$ The particle is slightly disturbed from its equilibrium position. Show that it will perform approximate simple harmonic motion and find the period of the motion.