In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.
Mathematically, Hooke's law states that
where
- x is the displacement of the end of the spring from its equilibrium position;
- F is the restoring force exerted by the material; and
- k is the force constant (or spring constant).
Hooke's law is named after the 17th century British physicist Robert Hooke. He first stated this law in 1676 as a Latin anagram,[1] whose solution he published in 1678 as Ut tensio, sic vis, meaning, "As the extension, so the force".When this holds, the behavior is said to be linear. If shown on a graph, the line should show a direct variation. There is a negative sign on the right hand side of the equation because the restoring force always acts in the opposite direction of the displacement (for example, when a spring is stretched to the left, it pulls back to the right).
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is the Mach number
is the speed of the source (the object relative to the medium) and
is the speed of sound in the medium