Restoring force and spring constant : When a spring is stretched or compressed from its normal position (x = 0) by a small distance x, a restoring force is produced in the spring to bring it to the normal position. According to Hooke’s law this restoring force is proportional to the displacement x and its direction is always opposite to the displacement.
where k is called spring constant.
(2) Expression for elastic potential energy :
Elastic potential energy
• If spring is stretched from initial position x1 to final position x2 then work done = Increment in elastic potential energy
Energy graph for a spring : It mean kinetic energy changes parabolically w.r.t. position but total energy remain always constant irrespective to position of the mass.