Set up differential equation for an oscillation of a spring using Hooke's and Newton's second law. Find the general solution of this equation and hence the expressions for period, velocity and acceleration of oscillation.

--- Consider a spring of negligible mass with one end fixed. A particle of mass m is attached to the free end. When the mass is displaced by a distance x (or l) from its equilibrium (natural) position, a restoring force acts on it. From Hooke's Law, the restoring force developed in the spring is ...