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!

Homework Help: Energy Problem involving simple harmonic motion

  1. Dec 11, 2007 #1
    1. The problem statement, all variables and given/known data
    The motion of a particle is described by x = 10 sin (piet +pie/2 ). At what time ( in second ) is the potential energy equal to the kinetic energy ?

    2. Relevant equations

    KE = 1/2 mv^2 PE=1/2 Kx^2
    3. The attempt at a solution

    V=pie10cos(piet + pie/3)
    V^2 = pie^2 100cos^2(piet+ pie/3)
    KE = mpie5ocos^2 (piet + pie/3)
    X^2 =100sin^2(piet +pie/2 )
    PE =k50 sin^2(piet +pie/2 )
    pie^2 100cos^2(piet+ pie/3) =K50 sin^2(piet +pie/2 )
    m/k * pie^2 = tan^2(piet +pie/2 )
    take square root of both sides of equation
    1/pie * pie = tan(piet + pie/3)
    piet + pie/3 =tan-1(1)
    solving for t i get a negative value where iam i going wrong.
  2. jcsd
  3. Dec 11, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    There appear to be a lot of algebraic errors throughout. Where has the m and k gone from the equation toward the end?

    EDIt: up to the this point you seem to be fine as far as I can tell:

    m/k * pie^2 = tan^2(piet +pie/2 )

    I just want to know how you got rid of the m and k in the next step?
  4. Dec 11, 2007 #3
    w(angular frequency) = (k/m)^0.5 so
    siince w = pie
    m/k = 1/pie
  5. Dec 11, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I tried a different approach and got the same answer. since the motion is SHM one would think that value +[itex]n2\pi[/itex] should work.
  6. Dec 11, 2007 #5
    what is n2PI is it equal to m/k ?
  7. Dec 11, 2007 #6


    User Avatar
    Homework Helper

    You can wright PE = 1/2*m*w^2*x^2 and KE = 1/2*m*w^2*(A^2 - x^2)
    When PE = KE, we get 2x^2 = A^2 or x = A/sqrt2. Put this value in the equation of SHM.
    A/sqrt2 = Asin(pi*t + Pi/2 ) or 1/sqrt2 = sin(pi*t + pi/2). Sin(pi/4) = sin(3*pi/4) = 1/sqrt2 To avoide negative time, take sin(3pi/4) = sin(pi*t + pi/2)
    That gives you t = 1/4 s.
    Last edited: Dec 11, 2007
  8. Dec 11, 2007 #7
    the anwser is 0.9 s
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook