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Simple harmonic motion

  1. Nov 3, 2014 #1
    • Member warned about posting without the template and with no effort
    For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law 6fedda8728eaf5ffe792a33a178a50ed.png and dc96864788dee12cac5cd92c0d799532.png


    i dont get this part 6d939d356c64eb78a89eab7090f86ab9.png which [PLAIN]http://upload.wikimedia.org/math/6/5/6/656fd81e91b7ad38db0c1f263dd5f4af.png[/B] [Broken]

    so can somebody explain it to me? Thank you
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Nov 3, 2014 #2

    vela

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    What don't you get?
     
  4. Nov 3, 2014 #3

    RUber

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    The first part is the solution to the differential equation.
    The second part is a recast of the solution with one function (cosine).
    If you let ##\frac{c_2}{c_1}=\tan \phi## this is the angle sum identity for cosine.
     
  5. Nov 6, 2014 #4
    6d939d356c64eb78a89eab7090f86ab9.png why? why "w'' = the square root of 'k' divided by 'm' i don't get this equation
     
  6. Nov 6, 2014 #5

    vela

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    Try plugging ##x(t) = A\cos(\omega t-\varphi)## into the differential equation.
     
  7. Nov 12, 2014 #6
    how do they people get this equation? 6d939d356c64eb78a89eab7090f86ab9.png , where does it come from? can you show me process of deducting this formula? THANKS!
     
  8. Nov 12, 2014 #7

    vela

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    Did you try plugging x(t) into the differential equation?
     
  9. Nov 12, 2014 #8

    RUber

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    It is simply a notational convenience. You could continue to use sqrt(k/m) everywhere but that gets messy.
     
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