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Differential equation

  1. Dec 4, 2006 #1
    How do I solve

    [tex]\ddot{\theta} = c \cos{\theta}[/tex]?
     
  2. jcsd
  3. Dec 4, 2006 #2

    Integral

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    Numerically. Try Runga Kutta, or for small angles Cos ( [itex] \theta [/itex]) ~ 1 so solve

    [tex] \ddot{\theta} = c [/tex]
     
  4. Dec 4, 2006 #3

    dextercioby

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    Multiply by [itex] 2\dot{\theta} [/itex] and then notice that you get

    [tex] \frac{d}{dt}\dot{\theta}^{2} = c\frac{d}{dt}{\sin\theta} [/tex]

    The rest is easy.

    Daniel.
     
  5. Dec 4, 2006 #4
    Is it? =P

    [tex]\dot{\theta}^2 = c_1 \sin{\theta} + c_2[/tex]?
     
  6. Dec 4, 2006 #5

    dextercioby

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    Yes, now separate variables and integrate.

    Daniel.
     
  7. Dec 4, 2006 #6

    HallsofIvy

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    "The rest is easy"!:rofl:
     
  8. Dec 4, 2006 #7
    Ok, so now I got the integral

    [tex]\int \frac{d\theta}{\sqrt{c - \frac{3g}{L}sin{\theta}}}[/tex]

    to solve. Any tip?
     
  9. Dec 4, 2006 #8

    dextercioby

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