# Changes

tidy up

It should be noted that in reality, Hooke's law is merely an approximation, and no physical spring actually has precisely this behavior. However, for most materials a version of Hooke's law holds for reasonable ranges of <math>\vec x</math>. This is called the ''elastic range'' of the material.

If a particle moves only under the influence of the force exerted by a spring, then Newton's second law (<math>\vec F = m \vec a</math>) implies that its displacement satisfies the second-order [[differential equation]] <math>m\ddot{\vec x} = - k \vec x</math>. ~~ ~~ This is solved by : <math>\vec x(t) = \vec x_0 \cos(\omega t+ \phi)</math>~~, ~~ where <math>\phi</math> is a phase shift and <math>\omega</math> is the angular frequency and is: <math>\omega = \sqrt{\frac{k~~/~~}{m}}</math> ~~is the frequency of oscillation: thus ~~ Thus the particle moves in a ~~"~~[[sine|~~sine wave~~sinusoidal]]~~" shape~~manner. ~~ ~~This is an example of simple harmonic motion.

[[Category:Physics]]

[[Category:Mechanics]]