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: How to show that the motion graph of a linear oscillator is an ellipse.

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The motion of a linear oscillator may be represented by means of a graph in which x is abscissa and dx/dt as ordinate. The histroy of the oscillator is then a curve
    a)show that for an undamped oscillator this curve is an ellipse
    b) show (at least qualitatively) that if a damping curve is introduced on gets a curve spiraling into origin.
    2. Relevant equations
    3. The attempt at a solution
    a) I got that
    Another student told me to "elimate the t's" to get
    x2/A2 +X2/(Aw)2 =1
    and that is total energy is E=1/2KA2 and w2=k/m then
    x2/(2E/k) +X2/(2E/m) =1

    First of all, I dont under stand how eliminated his t's. I do get that he found the eq of an ellipse, but how do I go from an eq with X and w to one with x and dx/dt?

    b)I have no sweet clue
  2. jcsd
  3. Oct 7, 2012 #2
    I suspect that his answer should read

    \frac{x^2}{A^2} + \frac{v^2}{A^2w^2} = 1

    To arrive at this rearrange the x and v equations so that only the sin and cosine functions are left on the right hand side. Then square both equations and add. \

    For part b you will want to add a damping constant to the equation of motion:

    m \frac{d^2x}{dt^2} = -kx - c \frac{dx}{dt}

    You will need to find solutions to this equation. From there you can find v, and plot x vs v.
  4. Oct 7, 2012 #3

    Ok a) makes total sense now
    b) In is c the damping constant? (we're using b) we have found in class that the solution to his comes in the fourm Aej(pt+α) is this what you mean?
  5. Oct 7, 2012 #4
    Yep, that's what I'm talking about.
  6. Oct 7, 2012 #5
    Ok then but Im still not sure where v is going to come from...
  7. Oct 7, 2012 #6
    Once you solve for x(t) then the velocity is just the derivative.
  8. Oct 8, 2012 #7
    Oh right. I get it. Thanks alot :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook