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Homework question concerning simple harmonic motion

  1. May 3, 2008 #1
    1. The problem statement, all variables and given/known data A system has a period of 3 seconds. The 4 kg mass oscillates with an amplitude of 0.7 meters. At what position is 50% of its energy in the form of kinetic energy and what is its velocity then?



    2. Relevant equations
    work = Potential energy + Kinetic energy
    (1/2)kA^2 = (1/2)kx^2 + (1/2)mv^2


    3. The attempt at a solution
    I found k = 17.55 Newton meters.
    So, I was thinking of two possible approaches:
    a.) (1/2)kA^2 - (1/2)kx^2 = (1/2)mv^2
    b.) kx^2 = mv^2

    I'm pretty sure I'd use my second idea. If that's right, what would I plug in for x? The amplitude?
     
  2. jcsd
  3. May 3, 2008 #2
    Yes, you are correct to use kx^2 = mv^2. Your term 0.5kA^2 is the same thing as 0.5kx^2, the only difference is that "amplitude" can mean more than 1 direction.

    So for example if your mass could go in either the X or Y direction, 0.5kA^2 = 0.5kx^2 + 0.5ky^2

    So just use option B.
     
  4. May 3, 2008 #3

    alphysicist

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    Homework Helper

    Hi robf224,

    I don't think you should use either of your two equations separately. The first equation contains the total energy, and the second has the 50% condition. But you now have two equations with two unknowns and can solve the two equations simultaneously to find both x and v.
     
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