Mass-Spring System

A mass-spring system is a trolley attached to two posts by two springs. When the trolley is displaced to one side and then released, it oscillates back and forth with simple harmonic motion.The frequency of oscillations depends on the mass and the spring constant k or stiffness of the spring.A larger mass would oscillate more slowly because of the inertia, and weaker springs would give less of a restoring force so the speed at any given displacement would be less.Assuming the spring obeys Hooke's Law the tension in the spring will be
T = -kx
where the minus indicates the tension always tries to restore the spring to its equilibrium position.By Newton II,
a = -kx/m = -(2πf)²x.
Rearranging givesf = (1/2π)√(k/m)