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Simple Harmonic Motion using total mechanical energy

  1. Jul 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A 250 gram mass is connected to a spring and executes simple harmonic motion. The period of motion is 0.5 seconds and the total mechanical energy is 0.50J. What is the amplitude of motion?

    2. Relevant equations
    ΔU = 1/2kx2

    3. The attempt at a solution
    I get

    1/2kx2 = 0.5J,

    then I get

    kx2 = 1.0J

    Not sure where to go from here. I do have the answer from the answer key, but I have no idea how to actually get the answer. I think I'm supposed to integrate something, but I'm not sure how to incorporate the time value into any equations.
     
  2. jcsd
  3. Jul 26, 2012 #2
    do you know another equation involving k that applies to your situation?
     
  4. Jul 26, 2012 #3
    kx=ma, perhaps? If so, should I use kx = m(dv/dt)? But then how will I obtain a value for velocity?
     
    Last edited: Jul 26, 2012
  5. Jul 26, 2012 #4
    what does the solution of the differential equation kx=ma look like? [Check your notes on simple harmonic motion, watch out for sign conventions]
     
  6. Jul 26, 2012 #5
    d/dt(kx)=d/dt(ma)
    k(dx/dt)=m(da/dt)
    kv(t)=m(da/dt)?
     
  7. Jul 26, 2012 #6
    a = dv/dt = d2x/dt2 would be a better route. da/dt is going in the wrong direction.

    ========


    the solution will be of the form x = F(t) where F will be a function that you recognise.
     
    Last edited: Jul 26, 2012
  8. Jul 26, 2012 #7
    x=ma/k? I am totally lost...

    I have ax=4. Am I on the right track?
     
  9. Jul 26, 2012 #8
    what do your notes say for how x varies in a system that is executing simple harmonic motion? There is something not quite right with your kx = ma. Not quite because it is normally expressed in an ever so slightly different way.
     
  10. Jul 26, 2012 #9
    F = -kx
    W = Fd =∫Fnetdx
    Wtotal = ΔK
    ΔU = 1/2kx2
     
  11. Jul 26, 2012 #10
    If y = sin(t) what is dy/dt, what about d2y/dt2
     
  12. Jul 26, 2012 #11
    dy/dt=cos(t), d2y/dt2=-sin(t)?

    Thank you for your help thus far, but it's 4AM over here in the EST timezone, so I must go to bed. I will check back on this thread in five hours or so.
     
  13. Jul 26, 2012 #12
    so how are y and d2y/dt2 related? is there anything that you have posted so far that looks similar?
     
  14. Jul 26, 2012 #13
    m(dv/dt)=k(dx/dt)
    m(dv/dt)=kv?
     
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