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Differential equation

  1. Feb 23, 2004 #1
    this is for a lab, but i wrote down the wrong equation. the lab was about attaching a 200 gram mass to a spring. we had to displace it so many cm, and than release it. we had to measure the period of the oscillations. but we are supposed to compare this measured period with a period obtained from the solution of the appropriate differential equation. i wrote down this for the diff eq, but im not sure if its right

    -kx -b(dx/dt)^2=m(d^2x/dt^2)

    is this the correct one? and if it is, where can i find the solution to this?
     
  2. jcsd
  3. Feb 23, 2004 #2
    The equation for undamped simple harmonic motion is:

    [tex]m\!\stackrel{..}{x} +\, \omega_0^2x = 0[/tex]

    It can be solved by attempting a solution of the form [itex]y = A\cdot \textrm{cos}(\omega x + \phi)[/itex]

    cookiemonster
     
    Last edited: Feb 23, 2004
  4. Feb 23, 2004 #3
    this needs to include friction. thats the b*v^2. i cant find anything anywhere that has a differential equation with friction.
     
  5. Feb 23, 2004 #4
    Just add a term:

    [tex]m\!\stackrel{..}{x} +\, \omega_0^2x + b\!\stackrel{.}{x}^2 = 0[/tex]

    cookiemonster
     
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