The restoring force from a spring displaced a distance x from its equilibrium point is given by Hooke's law
where m is the mass and k is the spring constant. This law holds (approximately) as long as x remains below the spring's elastic limit. Even when the elastic limit is not exceeded, pulling a coil spring far enough to uncoil it results in a much larger spring constant than the spring's "coiled" value.
The differential equation describing the spring's motion is
which is a simple harmonic oscillator with angular frequency
The potential energy stored in a compressed spring is
Hooke's Law, Spring Constant, Springs--Two Springs and a Mass, Springs--Two Springs in Parallel, Springs--Two Springs in Series, Springs--Three Springs and Two Masses, Springs--Three Masses
