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Thread: No solution for an arbitrary constant.

  1. #1
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    No solution for an arbitrary constant.

    Say I have found a general solution to an equation of motion, which is, simple harmonic motion.

    The general solution I have found is of the form:

    $\displaystyle x(t) = L+B\cdot cos(\omega t)+C\cdot sin(\omega t)$

    When inserting some (supplied) inital conditions, I am able to solve to find $\displaystyle B$ but cannot find a solution for $\displaystyle C$, does it follow that $\displaystyle C=0$?

    My initial conditions contain only the position when $\displaystyle t=0$, $\displaystyle x$ and no derivatives of it - this being the case

    $\displaystyle C\cdot sin(\omega t)=C\cdot sin(\omega \cdot 0)=0$

    I hope it does, because I'm stumped if not - If the question above is too vague, I can supply the full question. However, I want to solve it myself and this is why I have used generic formulae above.
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  2. #2
    A Plied Mathematician
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    What exactly are the conditions? Are they initial conditions?
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  3. #3
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    Yes. They are initial conditions.

    The formula is for a spring, I am given the height it is released from at $\displaystyle t=0$ only.
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  4. #4
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    I have worked this one out now. Thanks for the help.
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  5. #5
    A Plied Mathematician
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    You're welcome for whatever help I could provide.
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