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Air resistance Differential Equation Help

  1. Mar 15, 2005 #1

    $id

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    Hi guys

    I need help solving the following differential equation for air resistance

    d^2s/dt^2 + R ds/dt = g


    Where g = gravity I presume and R = k/m where k = resistance constant

    Using my limited knowledge I think that the auxiliary equation for this is

    Y^2+ RY = 0

    Y = 0 or R

    General Solution

    S = A + Be^Rt

    Which log graph would i need to plot to work out resistance constant.

    thanks a lot

    sid
     
  2. jcsd
  3. Mar 15, 2005 #2

    dextercioby

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    You meant "-R" and [itex]...e^{-Rt} [/itex] ("R" positive,i presume).

    Linearize the equation.U'll find R from the negative slope...

    Daniel.
     
  4. Mar 15, 2005 #3

    $id

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    Is the actualy equation correct though?

    Or am i missing something

    sid

    BTW by linearise i think you mean

    ln(S)=LnA + LnB -RT

    So a plot of Kn(S) against T for some values should yeild the gradinet at -R

    yeah ?
     
  5. Mar 15, 2005 #4

    dextercioby

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    Yes,for the second part.The initial equation may be correct,i don't know how u've gotten it.But the solution you had found was incorrect.

    Daniel.
     
  6. Mar 15, 2005 #5

    $id

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    So the general solution is wrong?
     
  7. Mar 15, 2005 #6

    dextercioby

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    For the homogenous eq.is correct

    [tex] s(t)=A+Be^{-Rt} [/tex],with R>0...

    Daniel.
     
  8. Mar 15, 2005 #7

    $id

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    well g is constant as it = to 10

    so isnt the equation homogenous in essence

    sid
     
  9. Mar 15, 2005 #8

    dextercioby

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    No,a homogenous is when the constant is 0.

    Daniel.
     
  10. Mar 15, 2005 #9

    $id

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    ok fair enough,

    The orginal differential equation is definate correct, it was taken from a book

    What do you reccomend for solving that equation

    sid
     
  11. Mar 15, 2005 #10

    dextercioby

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    You tried one way.Try differently.Make a substitution

    [tex] \frac{ds(t)}{dt}=:u(t) [/tex]

    Daniel.
     
  12. Mar 15, 2005 #11

    $id

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    Unfortunately i am not aware of that method

    the only ones i know are auxiliary equation, seperation of variables and intergrating factors

    Do you which one of those will work.

    sid
     
  13. Mar 15, 2005 #12

    dextercioby

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    Separation of variables...?Write the new equation.You'll see that the variables would be separated.

    Daniel.
     
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