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Differential equation.

  1. Oct 23, 2009 #1
    1. The problem statement, all variables and given/known data
    x(t) = Asin (Wt + z)
    Define values for A(amplitude) and z(angle) so that:
    x(0) = x0 and x´(0) = v0


    2. Relevant equations
    Chain rule.


    3. The attempt at a solution
    Im pretty sure I got the z part right:
    x(0) = Asin(z) = x0
    x´(0) = AWcos(z) = v0

    Solve simultaneous equations for z:

    sin(z)/cos(z) = (x0/a)(AW/v0)
    tan(z) = (x0W/v0)
    z = tan^-1(x0W/v0)

    As for the A part I have no idea how to go about solving it:

    Rearranging the x(0) equations for A
    Asin(z) = x0
    AWcos(z) = v0
    A=x0/sin(z)
    A=v0/Wcos(z)

    Now what?
     
  2. jcsd
  3. Oct 23, 2009 #2

    Mark44

    Staff: Mentor

    Substitute the value you got for z into the equation A sin z = x0. That will give you A sin(tan-1(x0W/v0) = x0. Then solve that equation for A, which will give you A in terms of x0, v0, and W.
     
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