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Damped harmonic oscillator

Damping Force & Total Energy. See attached file for full problem description.

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documentclass[a4paper]{article}
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begin{document}
title{Damped Oscillator}
date{}
author{}
maketitle
Newton's second law implies that:
begin{equation}label{diff}
begin{split}
&mfrac{d^{2}x}{dt^{2}}=-kx-2beta m frac{dx}{dt}Longrightarrow
&frac{d^{2}x}{dt^{2}} + 2beta frac{dx}{dt} + frac{k}{m}x =0
end{split}
end{equation}
If you insert a trial solution ...

Solution Summary

A detailed solution is given.

$2.19