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Simple Harmonic Motion Problem

  1. Apr 6, 2014 #1
    1. The problem statement, all variables and given/known data

    An object moving with harmonic motion has an acceleration of -2 m/s^2 when the elongation is 0.5 m. Determine the angular frequency and the velocity and acceleration for t=1s.

    2. Relevant equations

    a=-ω2x (1)
    x=Acos(ωt+θ) (2)
    a=-Aω2cos(ωt+θ) (3)

    3. The attempt at a solution

    I found ω using equation (1). My problem is from this point on. To find the velocity and acceleration for t=1s I need to find the value of A and θ. However, I cannot do so because I don't know the time for which a=-2m/s2 or x=0.5m. I believe I would have to assume that t=0 for the data given but I don't like to do that as it is not stated in the problem. So, my question is, am I missing something obvious here or is there missing information in the statement? Thanks a lot for your help.
     
  2. jcsd
  3. Apr 6, 2014 #2

    Simon Bridge

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    You know more equations than that - model the motion as a mass on a spring.
    You need to get the velocity etc as a function of position not time.
    Hint: look at the energy.
     
  4. Apr 6, 2014 #3
    Hi Simon: Not sure what you mean. First, problem does not state the mass. Second, the equations for kinetic and potential energy both depend on the amplitude which I don't think I can find with the given data. Incidentally, at this point in the curriculum I am not supposed to know about energy yet. In any case, I still think that the problem is not given me enough data to find a solution. Thanks for the suggestions though.
     
  5. Apr 6, 2014 #4
    It looks undetermined, if this is the full text of the problem. Even if you assume that the values are for t=0.

    When in this sort of doubt you can try to see if multiple sets of unknown parameters are compatible with the given data.

    For example, you can take
    A= 1m and θ = π/3
    or
    A=0.5 m and θ =0.

    Both sets of parameters will give you the x=0.5 m and a=-2 m/s^2 at t=0.
    But the values for v(1s) will be different.
     
  6. Apr 6, 2014 #5

    Simon Bridge

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    ... about what?
    ... it may not matter. The mass may cancel out.

    You may end up with several equations in which you have several unknowns - like mass and amplitude and initial phase.
    You solve them as simultaneous equations.

    This is often the case when it looks like there is not enough information.

    If that's the case them probably not enough data for your expected skill level.
    It is likely, then, that the extra information is assumed in the framework that SHM has been explained to you in class.

    i.e. maybe 0.5m is intended to be the initial displacement - the object is thus released from rest at x=+0.5.

    (It seems odd to do SHM before conservation of energy and energy stored in a spring.)
     
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