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Simple harmonic motion (doubt in the derivation of equation)

  1. Apr 17, 2010 #1
    F=-kx when talking about a mass at the end of a horizontal spring
    therefore ma=-kx
    rearranging we get a= -(k/m)x
    then it says if we define ω2=k/m we then have a generic form :
    a= -ω2x
    My question is what does "if we define ω2=k/m" mean? where does this come from?is it just any random assumption?
     
  2. jcsd
  3. Apr 17, 2010 #2

    Doc Al

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    Staff: Mentor

    They define it that way because they already know the answer. The solution to the differential equation ma=-kx (or m d2x/dt2 = -kx) will be a sinusoidal function with an angular frequency given by ω = √(k/m).
     
  4. Apr 17, 2010 #3
    I didn't get it.How do you find the angular frequency from the sinusoidal function of ma=-kx (or m d2x/dt2 = -kx ?
     
  5. Apr 17, 2010 #4

    Doc Al

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    Staff: Mentor

    Last edited by a moderator: Apr 25, 2017
  6. Apr 17, 2010 #5
    aah! great stuff,thanx.
     
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