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Math Help - could someone give me advice? differential equation.

  1. #1
    Newbie
    Joined
    Dec 2009
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    5

    could someone give me advice? differential equation.

    Hi im having problems with the following 2 question and was wondering if somebody could give me some help on how to do it. Im not the best at math so any help/advice/answer would be greatly appreciated. Feel free to move this thread if its in the wrong catagory.
    Totster.
    1. (a) Solve the following second order linear differential equation

    (d^2(
    x)/(d)t^2)+ 5(dx/dt) + 4x = 0

    subject to the initial condition
    x(0) = 0 and x˙(0) = 1. What type
    of damping does this motion illustrate?
    (b) Solve the following second order linear differential equation

    (d^2(
    x)/(d)t^2)+ x = cos(t)
    subject to the initial condition
    x(0) = 0 and x˙ (0) = 0. What type
    of motion do you find?
    2. A satellite undergoes an elliptic orbit about the Earth of mass
    M, with
    maximum distance 6
    R and minimum distance 3R from the Earth’s
    centre where
    R is the radius of the Earth.
    (a) Show that the minimum velocity
    vmin and the maximum velocity

    v
    max are given by

    v
    max = 2vmin = 2/3GM/R

    (b) Show that the eccentricity of the satellite is
    e = 1/3.

    Thanks

    Last edited by totster; April 6th 2010 at 06:13 PM. Reason: maybe in wrong catagory and I dont no how to change it to a different one.
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  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Quote Originally Posted by totster View Post
    Hi im having problems with the following 2 question and was wondering if somebody could give me some help on how to do it. Im not the best at math so any help/advice/answer would be greatly appreciated. Feel free to move this thread if its in the wrong catagory.
    Totster.
    1. (a) Solve the following second order linear differential equation

    (d^2(
    x)/(d)t^2)+ 5(dx/dt) + 4x = 0

    subject to the initial condition
    x(0) = 0 and x˙(0) = 1. What type
    of damping does this motion illustrate?

    The characteristic equation is r^2+ 5r+ 4= 0. Can you solve that? What do the solutions of that equation tell you about the solution to the differential equaiton?

    (b) Solve the following second order linear differential equation
    (d^2(
    x)/(d)t^2)+ x = cos(t)
    subject to the initial condition
    x(0) = 0 and x˙ (0) = 0. What type
    of motion do you find?
    2. A satellite undergoes an elliptic orbit about the Earth of mass
    M, with
    maximum distance 6
    R and minimum distance 3R from the Earth’s
    centre where
    R is the radius of the Earth.
    (a) Show that the minimum velocity
    vmin and the maximum velocity

    v
    max are given by

    v
    max = 2vmin = 2/3GM/R

    (b) Show that the eccentricity of the satellite is
    e = 1/3.

    Thanks

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