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Math Help - Ode

  1. #1
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    Ode

    Hi guys ,

    I am looking for some help with this ODE question below.Can anyone help ?

    d squared i / dt squared +900i = D Sin (wt)

    Assuming w squared is not = 900 determine i in terms of w, D and t
    when initial conditions are:
    i(0)= di/dt (0) = 0

    Can you show workings as i have got so far and got stuck.

    Rossco
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  2. #2
    Senior Member Peritus's Avatar
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    First solve the homogeneous equation

    (d^2/dt^2)i + 900*i = 0

    than assume a particular solution of the form i = A*cos(wt) + B*sin(wt), plunge it into the ODE, equate the coefficients thus finding A & B.

    the final solution is the sum of the homogeneous & particular solution.
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  3. #3
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    Hi Peritus

    Thanks for the advice.I have started along this line already but not sure
    if doing it correctly.

    If you have time can you complete so i can compare with my solution ?

    Thanks,
    Rossco
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  4. #4
    Senior Member Peritus's Avatar
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    Hi Rossco

    One nice thing about ODE's is the existence & uniqueness theorem (I leave it for you to google about it), in the case of this particular ODE it's conditions are satisfied for all t, the consequence of this is that if you find a solution to it is the single only correct solution, this allows you to check your solution by plunging it into the ODE and verifying that you get an equality.

    Tell me what exactly is your problem? Is it solving the homogeneous equation or finding the particular solution?

    There are a lot of solved examples of second order ODE's on the net and plenty of other resources, I'd suggest you use them.

    You can at least post your solution so that some member of this forum might help you. Being spoon fed will not get you anywhere.

    Take care, and sorry if I was too rude.
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  5. #5
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    I get the above down to -w^2 a cos(wt) -w^2 b sin(wt) = D sin(wt)

    The next stage is to calculate the co-efficients not sure what the co-efficients are for this .Can anyone help to solve ?

    Rossco
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rossco View Post
    I get the above down to -w^2 a cos(wt) -w^2 b sin(wt) = D sin(wt)

    The next stage is to calculate the co-efficients not sure what the co-efficients are for this .Can anyone help to solve ?

    Rossco
    No constant a is going to make that cosine term look anything like a sine term. So a = 0. Thus
    b = -\frac{D}{w^2}

    -Dan
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