A particle is attached between two ideal identical springs and the other ends of springs are kept fixed at points A and B on the horizontal plane. Springs are also horizontal such that the whole arrangement lies on the horizontal plane as shown in figure. Initially at t = 0 the particle is at point O and in this position both springs are unstretched then the particle is pulled very slowly perpendicular to the initial straight line AOB upto point P on the horizontal plane and released at t = t 0 .

(i) Work done by the external agent from t = 0 to t = t 0 to pull particle from point O to point P if spring constant of each spring is K is –