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Math Help - Having Trouble Setting up a System...

  1. #1
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    Having Trouble Setting up a System...

    ...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.

    "Suppose that the time rate of change (ROC) of a price M(t) of a product, minus inflation I(t) is proportional to the difference between Supply S(t) at time t and some equilbrium supply t.

    (If S>S_0 the supply is too large and cost 'will' decrease. If S<S_0 supply is too low and price 'will' increase)

    Also assume that the ROC in supply is proportional to the difference between the price P and some equilibrium P_0

    (If P>P_0 the price is too high and supply will increase. If P<P_0 the price is too low and supply will decrease)

    We've also got that F(t) = sinwt

    Now, this is what I have scribbled down in an attempt to get some working out, but I highly doubt that it is anywhere near correct, as I'm having trouble moving the knowledge of DEs from just straight questions into drawing stuff out of problems.

    dy/dt(M(t) - I(t))(s(t) - S_0) = 0
    I(t) = sinwt

    As I've, I'm well from confident about it Can anyone help out at all? TYVM
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  2. #2
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    Quote Originally Posted by teddydraiman View Post
    ...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.

    "Suppose that the time rate of change (ROC) of a price M(t) of a product, minus inflation I(t) is proportional to the difference between Supply S(t) at time t and some equilbrium supply t.

    (If S>S_0 the supply is too large and cost 'will' decrease. If S<S_0 supply is too low and price 'will' increase)

    Also assume that the ROC in supply is proportional to the difference between the price P and some equilibrium P_0

    (If P>P_0 the price is too high and supply will increase. If P<P_0 the price is too low and supply will decrease)

    We've also got that F(t) = sinwt

    Now, this is what I have scribbled down in an attempt to get some working out, but I highly doubt that it is anywhere near correct, as I'm having trouble moving the knowledge of DEs from just straight questions into drawing stuff out of problems.

    dy/dt(M(t) - I(t))(s(t) - S_0) = 0
    I(t) = sinwt

    As I've, I'm well from confident about it Can anyone help out at all? TYVM
    Have you read your post again after posting it? You designate the price with variable M and with variable P. Then F(t)=sin(wt) seems to be inflation I(t), or not? So this becomes difficult to follow and moreover what is the exact question?

    I assume you mean by the first part:

    \frac{dM}{dt}-I(t)=-K\cdot \left(S(t)-S_0 \right)

    K is a proportionality constant. And by the second part:

    \frac{dS}{dt}=M(t)-M_0

    And finally:

    I(t)=sin(wt)

    If this is correct you can substitute the second and last part in the first one and obtain a second order DE. Please check this and come back to shed some light on these dark postingshadows :-)

    Coomast
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  3. #3
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    Gah. I did mean that I(T) = sinwt, rather than F(T). And grud knows why I've switched between P and M for price.
    All the rest is correctly interpreted. Very sorry for the confusion.
    Last edited by mr fantastic; September 3rd 2009 at 05:04 AM.
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  4. #4
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    Quote Originally Posted by teddydraiman View Post
    Gah. I did mean that I(T) = sinwt, rather than F(T). And grud knows why I've switched between P and M for price.
    All the rest is correctly interpreted. Very sorry for the confusion.
    No problem I'm happy everything is sorted out with the question. OK, so can you write down the second order DE and solve it? It should look familiar....

    coomast
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