Conservation of Energy

The total energy of the ideal mass-spring system is constant:

$\displaystyle E$	$\displaystyle =$	$\displaystyle PE + KE$
	$\displaystyle =$	$\displaystyle \frac{1}{2} K A^{2} \left(\sin^2(\omega_0t + \phi) + \cos^2(\omega_0t + \phi)\right)$
	$\displaystyle =$	$\displaystyle \frac{1}{2} K A^{2}$

**Figure 2:** The interplay between PE and KE.
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``MUS 206: Mechanical Vibration'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).