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Driven Oscillation- Motion of a particle, with given equation.

  1. Jul 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Okay.. so I have tried to do this one but no luck.

    2. Relevant equations
    w= 2 * pi* v
    1/2 kA^2= 1/2mv^2 + mgh


    Alright so the question:

    The motion of a particle is given by x(t)= 25cm* cos 10t
    What time is the kinetic energy twice the potential energy?


    Not sure how to use a x(t) equation to incorporate mgh which deals motion in the y direction.

    Any guide would be appreciated.. Thanks!!
     
  2. jcsd
  3. Jul 6, 2009 #2

    turin

    User Avatar
    Homework Helper

    You are probably just suffering from notational inconsistency/ambiguity. I suspect:

    - The "v" in the equation for frequnecy is actually not a "v" at all, but rather Greek letter "nu". I.e., it is not velocity, but rather cyclic frequency. I would use "f" instead.

    - The "x" and "y" directions are arbitrary. And so, while "y" is typically chosen to represent vertical position, "x" is just as well. In fact, you have "1/2 kA^2" and "mgh" in your energy equation, and "y" does not appear anywhere. I suspect: A=h=x in your equations.

    - The equation of the motion of the particle has unitless time. I suspect that the "10" in the argument of the cosine should have some units.

    BTW, why did you call this "Driven Oscillation"?
     
  4. Jul 6, 2009 #3
    I just used the unit name, it's called Driven Oscillations and resonance.
    Okay... hmm
    so looking at it only with energy considerations... we have amplitude so we can do the equation:

    1/2KA^2= 1/2 mv^2 + mv^2

    ... but mass shouldnt be included in the equation :S
    so this is where I get stuck again!
    lol ahhh
     
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