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Total Energy Of A Spring-Mass System

  1. Jun 17, 2008 #1
    Hello everyone, I hope someone can help me with this simple harmonic motion question
    I've been trying it for about an hour now and I think i may have found the problem but I want to run it by someone else :)
    I'm taking this Phsyics 12U course (Uni prep for Ontario, Canada) through correspondence and all I have to go by are the work books that I have received.

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

    My work book gives me a bunch of formulas for harmonic motion, those formulas are what I am using to re-arrange and sub and so on.


    Prove that Max Speed of a mass on a spring is given by 2 * pi * f * A

    So after re-arranging and all that fun stuff I get as far as

    vmax= sqrt(k/m) * A


    ===============================================

    so now the speed of the mass will be at max when it is right at equilibrium (x = 0)
    and the potential energy will be zero and the kinetic energy will be max

    So then I get this formula using energy equations, (Ek = kinetic energy, m = mass)

    vmax = sqrt(2 * Ek / m)

    now we can get Ek another way, and that is using the total energy of the system equation and this is where i get hung up

    in my workbook, it has the total energy of the system as

    Et = kA^2

    the total energy is all kinetic in this case so we can sub Ek for Et

    so I try to plug that into

    vmax = sqrt(2 * Ek / m)

    and I end up with

    sqrt(2k/m) * A


    which kind of looks like the 2 * pi * f * A rearranged except for that useless 2 in the numerator! :@

    so then I research this using google and on wikipedia it has the total energy of a spring mass system as

    Et = (kA^2) / 2

    so this formula has the same thing except the 2 in the denominator
    I then check another site and it also has the 2 in the denominator

    and it clicks, i put this formula in the equation instead and it all works out!

    so is my workbook giving me bad information??

    is the total energy of a Spring Mass system given as

    Et = (k * A^2)

    or

    Et = (K * A^2) / 2

    ???

    thanks in advance for all of the help!
     
    Last edited: Jun 17, 2008
  2. jcsd
  3. Jun 17, 2008 #2

    alphysicist

    User Avatar
    Homework Helper

    Hi D3SI,

    Yes, you found the problem; there should be a (1/2) factor in the total energy formula.
     
  4. Jun 17, 2008 #3
    woot!

    thanks for the reply :)

    gunna have a talk with the adult ed people at the high school, looks like they dont check the books b4 using em :(
     
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