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    Damped harmonic oscillator

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    Damping force and total energy. See attached file for full problem description.

    © BrainMass Inc. brainmass.com June 3, 2020, 7:34 pm ad1c9bdddf
    https://brainmass.com/physics/periodic-motion/damping-force-total-energy-104548

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    documentclass[a4paper]{article}
    usepackage{amsmath,amssymb}
    newcommand{haak}[1]{!left(#1right)}
    newcommand{rhaak}[1]{!left [#1right]}
    newcommand{lhaak}[1]{left | #1right |}
    newcommand{ahaak}[1]{!left{#1right}}
    newcommand{gem}[1]{leftlangle #1rightrangle}
    newcommand{gemc}[2]{leftlangleleftlangleleft. #1right | #2
    rightranglerightrangle}
    newcommand{geml}[1]{leftlangle #1right.}
    newcommand{gemr}[1]{left. #1rightrangle}
    newcommand{haakl}[1]{left(#1right.}
    newcommand{haakr}[1]{left.#1right)}
    newcommand{rhaakl}[1]{left[#1right.}
    newcommand{rhaakr}[1]{left.#1right]}
    newcommand{lhaakl}[1]{left |#1right.}
    newcommand{lhaakr}[1]{left.#1right |}
    newcommand{ket}[1]{lhaakl{gemr{#1}}}
    newcommand{bra}[1]{lhaakr{geml{#1}}}
    newcommand{braket}[3]{gem{#1lhaak{#2}#3}}
    newcommand{floor}[1]{leftlfloor #1rightrfloor}
    newcommand{half}{frac{1}{2}}
    newcommand{kwart}{frac{1}{4}}
    newcommand{bfm}[1]{{bf #1}}
    renewcommand{imath}{text{i}}

    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 Summary

    A detailed solution is given that discusses the damping force and total energy.

    $2.19

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