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Proving SHM using energy

  1. Dec 1, 2007 #1
    1. The problem statement, all variables and given/known data

    i have a bead on a wire shaped by y=cx^2 where y is the height - use conservation of energy to show that the system unfergoes simple harmonic motion. - no friction!

    2. Relevant equations

    I think to prove its SHM i need to get an equation in the form acc= - w^2 x

    3. The attempt at a solution

    KE + PE = A constant
    1/2mv^2 + mgh = A constant
    1/2mv^2 + mgcx^2 = A constant

    ... is this right? i am pretty sure i need it in the above form them from that i know what w is and can work out the period of this moyion.
     
  2. jcsd
  3. Dec 2, 2007 #2
    please help - with this i cant do the rest of the question :s
     
  4. Dec 2, 2007 #3
    Well as you said above, you need to show that the system satisfy an equation of the form acc = - constant * position.
    More precisly something saying Z'' = - constant * Z. It doesn't matter what this constant exactly is, besides being a constant.
    The v in your equation from the the kinetic energy is the SPEED of the bead so it's not the derivative of your x. What is v then? What happens if you plug that expression for v into your equation:

    1/2mv^2 + mgcx^2 = constant

    then taking the time derivative, so get something with dobbel derivative which is what you are seeking.
     
  5. Dec 2, 2007 #4
    what do i plug in for v? im totally confused...
     
  6. Dec 2, 2007 #5
    It's the length of the velocity vector, so it's
    v^2 = x'^2 + y'^2
    where x' and y' are the velocities in the x- and y- direction respectivly (ie time derivatives of x and y resp.). What is y' in this case?
     
  7. Dec 2, 2007 #6
    y' = 2xcx' ?
     
  8. Dec 2, 2007 #7
    ahhh -= please help somebaody - its in for tomrrow
     
  9. Dec 2, 2007 #8
    This is correct.
     
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