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Math Help - Need Help in this Numerical Methods question

  1. #1
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    Need Help in this Numerical Methods question

    Hi,
    Below is the questions :



    Can somebody show me the working on how to solve it. Thank you.
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  2. #2
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    let k = \frac{c}{m}

    \frac{dv}{dt} = g - kv

    \frac{dv}{g - kv} = dt

    \frac{-k}{g - kv} dv = -k \, dt

    \ln|g - kv| = -kt + C_1

    g - kv = e^{-kt+C_1} = e^{C_1} \cdot e^{-kt}

    g - kv = C_2e^{-kt}

    v = \frac{1}{k}\left(g - C_2e^{-kt}\right)

    v = \frac{mg}{c} \left(1 - C_3e^{-kt}\right)

    sub in your given data and determine the values of C_3 and k.
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  3. #3
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    thx for the simplified equation. But, still I am unclear of where do I replace the 'h' value that is given & the question is asking me the 'time' right, not velocity?
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  4. #4
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    Differential equation

    Hello hus2020
    Quote Originally Posted by hus2020 View Post
    thx for the simplified equation. But, still I am unclear of where do I replace the 'h' value that is given & the question is asking me the 'time' right, not velocity?
    If h represents the displacement (the height perhaps?), then v =\frac{dh}{dt}, and you'll need to integrate again to get h in terms of t.

    Grandad
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  5. #5
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    The problem is asks you to do 5 steps of a numerical integration of a differential equation. There are many different algorithms for that: Euler method, second order Runge-Kutta, fourth order Runge-Kutta, Adams-Bashforth, etc. Since none of us took the course YOU are taking, none of us know which algorithm you would be expected to use. We didn't attend the classes! Hopefully you did.
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  6. #6
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    yes, the question requires to use the Euler's method since the others are not taught yet.
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