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Finding amplitude of oscillation with only k, x, v, and a

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    An oscillating system of a block attached to a string where k = 400 at some time t has a position x of 0.1 m, velocity of -13.6 m/s, and accel. of -123 m/s^2. Find the amplitude of the motion. Do not use energy.


    2. Relevant equations
    x = Acos(wt + phi)
    v = -Awsin(wt + phi)
    a = -Aw^2cos(wt + phi)

    3. The attempt at a solution
    I can solve for omega by using sqrt(-a / x), we still have 3 unknowns A, t, and phi. We have 3 equations, but they are not linear equations so I don't know how to solve them simultaneously. What other method is there that I can use since I can't use energy?
     
  2. jcsd
  3. Jan 30, 2013 #2

    tiny-tim

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    Hi PhizKid! :smile:
    substitute the given values for x v and a

    then you have three linear equations …

    start eliminating variables :wink:
     
  4. Jan 30, 2013 #3
    But these are trig functions. Doesn't this make the equations non-linear? I'm not sure how to eliminate variables that have trig functions in them.
     
  5. Jan 30, 2013 #4

    tiny-tim

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    treat cos(wt + phi) and sin(wt + phi) as being variables in their own right! :smile:
     
  6. Jan 30, 2013 #5
    This doesn't work. When I simplify the equations for x and a, they are both identical:

    alpha = cos(wt + phi)
    beta = sin(wt + phi)

    0.100 = A * alpha
    0.100 = A * alpha
    0.388 = A * beta

    So it's really 2 equations with 3 unknowns... :(
     
  7. Jan 30, 2013 #6
    There is an identity relating sin and cos. Use it.
     
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