improper_umbrella.tex
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	\documentclass[12pt]{article}

	\begin{document}

	$$
	E=\frac{1}{2}K\left( \frac{1}{\sin\omega_0}\right) ^2 \left( \cos\omega - \cos\omega_0\right) ^2 \qquad \omega_0 \neq 0^o
	$$

	$$
	E=K\left( 1-cos\omega\right) \qquad \omega_0 = 0^o
	$$

	\end{document}