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Question about this simple harmonic motion problem

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data

    A particle with a mass of 65 g is moving with simple harmonic motion. At time t = 0, the particle is at its extreme positive displacement of 18.0 cm. The period of the motion is 0.600 s. Find the vecocity of the particle at t = 1.35 s

    2. Relevant equations

    (1). ω=2∏/T or
    (2). ω=√k/m

    (3). x=Acos(ω∏+δ)
    (4). v=-Aωsin(ω∏+δ)

    3. The attempt at a solution

    First question: to find ω, why don't I get the same answer for both equations 1 and 2?

    With equation 1 I get 10.47 (which I think is correct) and with eqn. 2 I get 7.45.

    Second question: How do I find the phase change for this problem? I tried to set the displacement equation equal to zero at t=0 and im getting ∏/2 but it seems that the only way to get the correct answer for the problem is to have zero phase change.
     
  2. jcsd
  3. Apr 28, 2013 #2

    TSny

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    It will help if show your calculations. In particular, how did you determine the value of k to use in eqn. 2?

    The problem states that the particle is at its extreme positive displacement at t = 0.
     
  4. Apr 28, 2013 #3

    SteamKing

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    How do you know what k is?
     
  5. Apr 28, 2013 #4
    I was thinking I could use hooke's law to find k.


    Tsny...

    I guess i'm just confused at finding phase changes.
     
  6. Apr 28, 2013 #5

    TSny

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    What does the equation x = Acos(ωt+δ) become for t = 0? Knowing that x is at it's maximum positive value at t = 0, what can you conclude about the value of δ?
     
  7. Apr 28, 2013 #6

    SteamKing

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    But how did you get a value of k to calculate omega of 7.45?
     
  8. Apr 28, 2013 #7
    Using F=kx

    0.65N=k(.18)

    k=3.61

    ω=√3.61/.065=7.45



    TSny... I think I see what you're saying. x would equal 18 at t=0.

    so 18cm = Acos(δ) ?


    Also, how do you quote two people in one reply?
     
  9. Apr 28, 2013 #8

    TSny

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    But you can't assume that the force acting on the particle is the weight of the particle. The simple harmonic motion might be due to a spring, and the force would be whatever the force of the spring happens to be for a given value of x.

    What does "A" stand for in this equation? What is the value of A?

    Pause your cursor over the "M" button next to the "Quote" button in the lower right corner and instructions will appear.
     
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