Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Harmonic Motion Brain Teaser

  1. Jul 22, 2004 #1


    User Avatar

    I saw this in an old, junior-level, classical mechanics
    textbook and haven't been able to figure it out.

    A particle undergoing simple harmonic motion has a velocity:


    when the displacement is:


    and a velocity


    when the displacement is:


    What is the angular frequency and the amplitude of the motion in terms of the given quantities?

    I know the solution to the SHM wave equation is:

    x(t) = A \cdot sin( \omega t + \phi )\end{equation}[/tex]

    And that:

    dx(t)/dt = A \omega \cdot cos( \omega t + \phi )\end{equation}[/tex]

    But can't see how to express omega or A in these terms.
    Last edited: Jul 22, 2004
  2. jcsd
  3. Jul 22, 2004 #2
    If x = A.sin(w.t) then

    x1 = A sin(w.t1)
    x2 = A.sin(w.t2)
    dx/dt 1= A.w.cos(w.t1)
    dx/dt 2 = A.w.cos(w.t2)

    I am not going to do it but there appears to be enough information , to eliminate t1,t2 and get A and w.
    For instance a) and c) can eliminate t1 , b) and d) eliminate t2 .
    Last edited: Jul 22, 2004
  4. Jul 22, 2004 #3

    Doc Al

    User Avatar

    Staff: Mentor

    Apply what you know. I'll get you started. You are given: At time [itex]t_1[/itex] the displacement is [itex]x_1[/itex] and the speed is [itex]v_1[/itex]. (I didn't like your notation, so I changed it. :smile: )

    So... just plug into your SHM equations:
    [itex]x_1 = A sin(\omega t_1)[/itex]
    [itex]v_1 = A \omega cos(\omega t_1)[/itex]
    Combine these equations to get a relationship between [itex]\omega[/itex] and A.

    Now do the same for time [itex]t_2[/itex], and then you should be able to solve for [itex]\omega[/itex] and A.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook