A light spring of natural length \(a\) and modulus of elasticity \(20mg\) stands vertically on a horizontal plane. The lower end of the spring is fixed to the plane. A particle of mass \(m\) is attached to the upper end of the spring.

The particle is pushed vertically downwards until the length of the spring is \(\dfrac{3a}{5}\). The system is then released from rest.

Find the maximum extension of the spring in the subsequent motion.