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How to find acceleration or displacement with respect to time?

  1. Apr 8, 2005 #1
    [tex]
    a(x)= kx + 1
    [/tex]
    where [tex]a(x)[/tex] is acceleration with respect to displacement along the x-axis and [tex]x[/tex] is the displacement itself while k is the constant.

    How to find acceleration or displacement with respect to time?
     
    Last edited: Apr 8, 2005
  2. jcsd
  3. Apr 8, 2005 #2

    dextercioby

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    Use the definition of acceleration to write the ODE.Depending on that sign of "k",the answer for x(t) is a linear comb.of complex or real exponentials...

    Daniel.
     
  4. Apr 8, 2005 #3

    dextercioby

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    Plus a constant (the ODE is nonhomogenous).

    Daniel.
     
  5. Apr 8, 2005 #4
    I can't figure out the ODE. Can you help me?
     
  6. Apr 8, 2005 #5
    acceleration is the second derivative of x wtr to time :

    [tex] \ddot{x} = kx + 1[/tex]

    [tex]\ddot{x} -kx -1 = 0[/tex]

    Can you solve it from here. You will need to set up the associated caracteristic equation and based upon the sign of k you will get a linear combination of exponentials or complex exponentials

    marlon
     
  7. Apr 8, 2005 #6

    dextercioby

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    The nonhomogeneity part is usually left in the RHS...

    Daniel.
     
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