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Second Order Equations Can Anybody help me? Greatly appreciated!

  1. Dec 30, 2006 #1
    Second Order Equations!! Can Anybody help me?? Greatly appreciated!

    1. The problem statement, all variables and given/known data
    Interpret x(t) as the position of a mass on a spring at time t where x(t) satisfies

    x'' + 4x' + 3x = 0.
    Suppose the mass is pulled out, stretching the spring one unit from its equilibrium position, and given an initial velocity of +2 units per second.

    (A) Find the position of the mass at time t.
    (B) Determine whether or not the mass ever crosses the equilibrium position of x = 0.
    (C) When (at what time) is the mass furthest from its equilibrium position? Approximately how far from the equilibrium position does it get?

    2. Relevant equations
    Previous problems on this homework set include transforming the initial value problem into a solution that looks partially like the following:

    y = (1/3)e^(-4t) + (2/3)e^(-4t)

    3. The attempt at a solution

    I've attempted the following:
    x" + 4x' + 3x = 0 --> r^2 + 4r + 3 = 0, solved for r

    r = -3 or -1
    therefore y=e^(-3t) , y=e^(-t)
    y(t) = Ae^(-3t) + Be^(-t)

    solved for A and B both = -1/2

    however, I'm not sure that this is right.

  2. jcsd
  3. Dec 30, 2006 #2


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    Homework Helper

    Does it satisfy the differential equation and boundary conditions? If so, it's probably right.
  4. Dec 30, 2006 #3
    so to find the position at t, i just solve for y in terms of t? like
    t = something

    also, how would i show if the mass crossed equilibrium at x = 0?
  5. Dec 31, 2006 #4


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    Homework Helper

    No, y(t) is the position at t. And you seem to be using x and y to refer to the same thing. Try graphing the function to see if it crosses 0.
  6. Dec 31, 2006 #5
    Or just set it equal to zero and see if there is a solution.
  7. Dec 31, 2006 #6
    thanks! i got it you guys :)
    thanks for all the help!
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