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Homework Help: Simple harmonic motion problem help.

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data

    particle experiencing SHM with frequency f= 10 hz
    find the displacement x at any time t for the following initial conditions.
    @ t=0 x=0.25m v=0.1 m/s

    2. Relevant equations


    3. The attempt at a solution

    So with frequency I find ω which then is subbed into the x=Asin(ωt+∅) @ t=0 to yield 0.25=Asin(∅).

    I then get v=Aωcos(ωt+∅) and sub in for v and t and ω and get 0.25=A(20∏)cos(∅)


    I then divide these equations by each other and rearrange to get:

    arctan(50∏)= ∅

    then with this I go back to 0.25=Asin(∅) and sub in ∅ rearrange to solve for A and its wrong! I get x=(0.16)sin(20∏t+1.56).

    answer in book says x=0.25cos(20∏t)+0.00159sin(20∏t). it says also acceptable solutions would be x=0.25sin(20∏t+1.56) and its cos variant.

    can someone please help I am confused about how they got this answer and how it is in that form.
  2. jcsd
  3. Oct 13, 2012 #2
    I like the books answers, I think you made a math error.

    Edit, I like the books first answer, still can't get the books second expression to work?

    The 1.56 in the books answer should be 1.5644?
    Last edited: Oct 13, 2012
  4. Oct 13, 2012 #3
    hurmm but why would Amplitude be 0.25 when it has a velocity that is not 0 meaning it is not at its maximum or minimum? and yes in the book they round.
  5. Oct 13, 2012 #4
    Because they give you the initial conditions at some point between max and min. The books answers (at least the first one) work when you properly substitute t = 0.
  6. Oct 13, 2012 #5
    While [itex]x(t)=A\sin(\omega t+\phi)[/itex] is a correct general solution to the harmonic oscillator, [itex]x(t)=A\cos(\omega t)+B\sin(\omega t)[/itex] is also correct and has the added bonus that [itex]x(0)=A[/itex] and [itex]x'(0)=B\omega[/itex].

    You can go from one to the other by using the identitiy:
    and going from [itex]x(t)=B\cos(\omega t+\phi)[/itex] can be done with
    Last edited: Oct 13, 2012
  7. Oct 13, 2012 #6
    The reason you can't get the books answer is because you used .25m for the velocity instead of .1m/s.
  8. Oct 14, 2012 #7
    thank you all this is more clear now!
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