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A simple harmonic motion is described by the displacement funtion

  1. Sep 5, 2008 #1
    Equation given


    u(t) =0.2 cos (wt) + 0.5 sin (wt), where w=3pi rad/s and displacement is in feet.

    Describe the same motion using amplitute/phase format.
    Describe the same motion using complex notation
    For t =0.4 sec calculate u


    How do you calculate u? and how do you describe the motion using amplitute and phase format based on the equation given?



    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 5, 2008 #2
    you need to show that you've made an effort to solve it yourself.
     
  4. Sep 5, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    For goodness, sake, certainly you know what "evaluate a functions" means!
     
  5. Sep 5, 2008 #4
    sorry I am not use to this so I will post my attempt to solve the problem
     
  6. Sep 5, 2008 #5
    I used the equation u(t) = Asin(wt+0)

    I solved for displacement first u(t) = 0.5sin(3pi)(.4sec)+ 0


    u (t) = 0.0328 and that is the answer for the first question but what I dont understand it that there is a cos cosine in the inital equation. So do I have to solve the cosine too inorder to get inorder to get the displacement or I am okay with this equation u (t) = Asin (wt + 0)
     
    Last edited: Sep 5, 2008
  7. Sep 5, 2008 #6
    If I were to describe the motion I would draw a picture of the sinusoidal wave and let the .5 and .2 graphed together showing waves and then I would say that a b sin wt is always 90degrees ahead of acos wt. But the sum of a cos wt and b sin wt produces a sinusoid of the same frequency....is this is correct
     
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