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Math Help - Nonlinear method for boundary value problems of a constant function.

  1. #1
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    Nonlinear method for boundary value problems of a constant function.

    the question Im having a hard time dealing with is this equation
    y"(t)=-g where g is the gravity at 9.8m/s^2
    and the boundaries are
    y(0)=0.9144 and y(3)=0

    how to solve this problem? I am having trouble with runge kutta since it is only a constant function? what to do pls?
    I need to know how many shots to and the graph. thanks
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  2. #2
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    Re: Nonlinear method for boundary value problems of a constant function.

    Hello, Marcorupert!

    From your title, you're making the problem sound trickier than it is.


    y"(t)\,=\,\text{-}g\;\text{ where }g\text{ is the accel'n due to gravity at }9.8\text{m/s}^2

    \text{and the initial conditions are: }\,y(0)\,=\,0.9144\,\text{ and }\,y(3)\,=\,0 .

    \text{Find }y(t).

    We have: . y''(t) \:=\:\text{-}9.8

    Integrate: . y'(t) \:=\:\text{-}9.8t + C_1

    Integrate: . y(t) \:=\:\text{-}4.9t^2 + C_1t + C_2


    We are told that y(0) = 0.9144\!:
    . . \text{-}4.9(0^2) + C_1(0) + C_2 \:=\:0.9144 \quad\Rightarrow\quad C_2 \,=\,0.9144

    We are told that y(3) = 0\!:
    . . \text{-}4.9(3^2) + C_1(3) + 0.9144 \:=\:0 \quad\Rightarrow\quad C_1 \,=\,14.3952


    Therefore: . y(t) \;=\;\text{-}4.9t^2 + 14.3952t + 0.9144
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  3. #3
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    Re: Nonlinear method for boundary value problems of a constant function.

    Thanks But I need to know the first shot of the graph in nonlinear method. :/
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