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Displacement and acceleration ( SHM? )

  1. Jul 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A small body is undergoing simple harmonic motion on a frictionless horizontal surface with an amplitude of 0.13m. At a point 0.05 m from equilibrium the velocity is 0.24 m/s. a.) what is the period?
    What is the displacement and acceleration when the velocity is ±0.10 m/s




    2. Relevant equations

    T = 2∏ √[itex]\frac{l}{g}[/itex]

    Displacement = [itex]\frac{a}{\frac{-4∏^{2}}{T^{2}}}[/itex]

    acceleration = [itex]\frac{v^{2}}{A}[/itex]



    3. The attempt at a solution

    T = 2∏ √[itex]\frac{0.05m}{g}[/itex]

    T = 0.45 S

    Displacement = [itex]\frac{0.08 m/s^{2}}{\frac{-4∏^{2}}{0.45 S^{2}}}[/itex]
    = -4.10 x [itex]10^{-4}[/itex] m

    acceleration = [itex]\frac{0.10m/s^{2}}{0.13m}[/itex]
    = 0.08 m/[itex]s^{2}[/itex]


    how is it?
     
  2. jcsd
  3. Jul 8, 2012 #2

    cepheid

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    This is the wrong equation. This is the equation for the period of oscillation of a pendulum of length l. Since the object in your problem is oscillating horizontally, g is not going to come into it.
     
  4. Jul 8, 2012 #3
    so the other two equation looks good except for the period?

    i dnt think i can use 2∏√[itex]\frac{m}{k}[/itex] ??
     
  5. Jul 8, 2012 #4

    cepheid

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    There are particular expressions for position vs. time, velocity vs. time, and acceleration vs. time that apply to SHM. To me, using these is the quickest way to solve the problem.
     
  6. Jul 8, 2012 #5
    the basic equations? like:

    a = [itex]\frac{Δv}{t}[/itex]

    displacement = vt

    v = [itex]\frac{d}{t}[/itex]
     
  7. Jul 8, 2012 #6

    cepheid

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    No, of course not. These equations don't describe oscillation. Can you think of functions that do?
     
  8. Jul 8, 2012 #7
    so the relevant equations i mentioned in the op has nothing to do with the problem statement?
     
  9. Jul 8, 2012 #8

    ehild

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    Start with the expression of the displacement as function of time in case of simple harmonic motion. Do you know it?

    http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html


    ehild
     
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