Simple Harmonic Motion cont.

The sinusoidal motion of the tuning fork is called simple harmonic motion, which is the simplest form of motion in vibrating systems.
If the displacement of a vibrating system is sinusoidal, i.e. $x = \cos(\omega t)$ , we may use Newton's third law to determine the frequency of the system. That is:

$\displaystyle ma$ $\displaystyle =$ $\displaystyle -kx$

$\displaystyle -\omega^2\cos(\omega t)$ $\displaystyle =$ $\displaystyle -\frac{k}{m}\cos(\omega t)$

$\displaystyle \omega$ $\displaystyle =$ $\displaystyle \sqrt{\frac{k}{m}}$

That is, the frequency is proportional to the square root of the ratio of the stiffness (or spring constant), (given in Newtons per meter), to the mass, .

``CMPT 889: Lecture 2: Sinusoids'' by Tamara Smyth, Computing Science, Simon Fraser University.

$\displaystyle ma$	$\displaystyle =$	$\displaystyle -kx$

$\displaystyle -\omega^2\cos(\omega t)$	$\displaystyle =$	$\displaystyle -\frac{k}{m}\cos(\omega t)$

$\displaystyle \omega$	$\displaystyle =$	$\displaystyle \sqrt{\frac{k}{m}}$