1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kinetic Energy from a Simple Harmonic motion and spring

  1. Jun 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is x = 1.4×10−2 m, what is the kinetic energy of the block?

    2. Relevant equations

    KE=1/2mw^2A^2sin^2(wt+phi)
    a=(k/m)x
    w=(k/m)^1/2


    3. The attempt at a solution
    I have everything for the equation except for phi and and the amplitude A. I have found a=10.23 m/s2 and w=27.0327rad/s but I am stuck on how to find phi and A. Is there a relationship between the initial equilibrium position for finding A or phi?

    Thanks for the help!
     
  2. jcsd
  3. Jun 15, 2016 #2

    BiGyElLoWhAt

    User Avatar
    Gold Member

    What's wrong with ##PE = 1/2 k x^2##?
    You have the amplitude, so you know the total energy. (Yes, you do have the amplitude)
     
  4. Jun 15, 2016 #3

    cnh1995

    User Avatar
    Homework Helper

    You do have A.
    What will be the KE of the block at t=0? Put it in this equation to get phi.
     
  5. Jun 15, 2016 #4
    To use PE=1/2kx^2 wouldn't I need the x at
    Is A= 0.014m?
     
  6. Jun 15, 2016 #5
     
  7. Jun 15, 2016 #6

    BiGyElLoWhAt

    User Avatar
    Gold Member

    No. When it's stretched initially, prior to letting go, what is the KE? At which point in the cycle of a general harmonic oscillator is the KE equal to this value?

    Then you're looking for the KE at the point x = .014m. So you know x for the PE, as you know at which point you want to look at.
     
  8. Jun 15, 2016 #7
    Oh I got it now!! Thanks so much !! :)
     
  9. Jun 15, 2016 #8

    BiGyElLoWhAt

    User Avatar
    Gold Member

    No problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Kinetic Energy from a Simple Harmonic motion and spring
Loading...