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Math Help - Help on solving differential equations...

  1. #1
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    Help on solving differential equations...

    I am doing a project on projectiles in sport and have set up the following differential equations when investigating the projectile of a golf ball with air resistance:

    mx'' = -kx' and my'' = -mg -ky'

    with initial conditions:
    x(0)=0
    x'(0)=u0=ucos(alpha)
    y(0)=0
    y'(0)=vo=usin(alpha)

    Could someone help me solve these differential equations and show me the method in which it is done. I am really not sure how to do them.

    Thanks
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  2. #2
    Eater of Worlds
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    m\frac{d^{2}t}{dt^{2}}=-kx

    has well known solutions of

    x(t)=C_{1}cos(\sqrt{\frac{k}{m}}t)+C_{2}sin(\sqrt{  \frac{k}{m}}t)

    Now, find x'(t) and use your initial conditions to find C_{1}, \;\ C_{2}
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  3. #3
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    Sorry can you explain that please. Not sure what you mean. Could you go through solving each equation step by step if possible please, i have attempted them and must have gone wrong at one of the early steps...

    Thanks
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  4. #4
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    Quote Originally Posted by galactus View Post
    m\frac{d^{2}t}{dt^{2}}=-kx

    has well known solutions of

    x(t)=C_{1}cos(\sqrt{\frac{k}{m}}t)+C_{2}sin(\sqrt{  \frac{k}{m}}t)

    Now, find x'(t) and use your initial conditions to find C_{1}, \;\ C_{2}
    Big G, you've misread the right hand side of the DE. It's x', not x.
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