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An object is undergoing simple harmonic motion

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    An object is undergoing simple harmonic motion with period 1.190 and amplitude 0.640

    At t=0 the object is at x=0 . How far is the object from the equilibrium position at time 0.475 ?



    2. Relevant equations



    3. The attempt at a solution

    x=Acos(ωt+∅)

    x= 0.640cos(2∏/1.190*.475)=.639

    The answer however is .379

    What am I doing wrong?

    Thank you

    - higgenz
     
  2. jcsd
  3. Apr 21, 2012 #2

    Curious3141

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    At t = 0, x = 0. What should the value of ∅ be?

    You'd be better off modelling the motion as x = Asin(ωt)
     
  4. Apr 21, 2012 #3
    Can you explain why you would use sin?
     
  5. Apr 21, 2012 #4

    Curious3141

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    You're told that at t = 0, x = 0. Sketch the curves of x = Asin(ωt) and x = Acos(ωt) with t representing the horizontal axis and x, the vertical. Which of them passes through the origin (0,0)?

    It's OK to use the phase-shifted cosine function x = Acos(ωt + ∅) as long as you calculate the value of the phase shift ∅. But you didn't.
     
  6. Apr 21, 2012 #5
    I was a bit confused on how to calculate ∅

    I know the formula for ∅ is arctan(-vox/ωxo)

    But isnt the initial velocity zero which would make it ∅= to 0 ?
     
  7. Apr 21, 2012 #6

    Curious3141

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    Don't get tied up in formulas you memorise. You must clearly understand the derivation of each formula you use, otherwise you'll use them in the wrong context.

    Go back to what you wrote. x = Acos(ωt + ∅).

    Now put t = 0 and x = 0 to get 0 = Acos(∅). So what should ∅ be?

    Use this value of ∅ and try to rework your answer. You'll get a negative value, but it doesn't matter - they just want the numerical magnitude.
     
  8. Apr 21, 2012 #7
    Excellent I got the answer than way as well. I appreciate you helping me out, and teaching me an alternative method!

    Higgenz
     
  9. Apr 21, 2012 #8

    Curious3141

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    You're welcome. :smile:
     
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