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Hooke's Law

102 bytes added, 21:05, 13 December 2016
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 wavesinusoidal]]" shapemanner. This is an example of simple harmonic motion.