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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
where is the kinetic energy and is the potential energy. Hooke's law is the potential energy of the spring itself: = where is the spring constant. The potential energy from gravity, on the other hand, is determined by the height of the mass. For a given angle and displacement, the potential energy is:
Potential energy is the energy by virtue of an object's position relative to other objects. [6] Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential.
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In classical physics, a spring can be seen as a device that stores potential energy, specifically elastic potential energy, by straining the bonds between the atoms of an elastic material. Hooke's law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension ...
When the spring is stretched or compressed, kinetic energy of the mass gets converted into potential energy of the spring. By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic energy of the mass is zero. When the spring is released, it tries to ...
In the animation with the two circling masses there is a back and forth oscillation of kinetic energy and potential energy. When the spring is at its maximal extension then the potential energy is largest, when the angular velocity is at its maximum the kinetic energy is at largest. With a real spring there is friction involved.
In a real spring–mass system, the spring has a non-negligible mass.Since not all of the spring's length moves at the same velocity as the suspended mass (for example the point completely opposed to the mass , at the other end of the spring, is not moving at all), its kinetic energy is not equal to .