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Simple pendulum

  1. Mar 31, 2004 #1
    hello friends,

    I have a question on the simple undamped and undriven pendulum. I see that according to the website:


    the angle of rotation, Theta(t), can be expressed in terms of the starting angle using the small angle approximation sin(theta) = theta.

    my question is, what is the ratio of successive thetas if we measure theta in increments of half periods ? the website shows:

    theta(t) = theta(t=0)*cos(wt+phi)

    i am interested in the ratio: theta(t=T)/theta(t=0) = cos(wt+phi)

    if we substitute w = sqrt(g/L) and t=T = 2*pi*sqrt(L/g) into the right side of this ratio we get:

    ratio = cos(2*pi + phi)

    but cos(2*pi) = 1.0.

    I dont see where i am going wrong since shouldnt the angle decrease over time until it is zero and the pendulum is stopped.

    I am curious to see if the ratio of successive theta's is constant.

    Last edited by a moderator: Apr 20, 2017
  2. jcsd
  3. Mar 31, 2004 #2
    The pendulum is UNdamped. No air resistance, no loss of energy. Real pendulums do indeed act like you think -- they stop eventually -- but this is only a theoretical pendulum.
  4. Mar 31, 2004 #3
    i see that without friction, the pendulum swings forever and the ratio is 1.0 as the equations show.
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