Results 1 to 3 of 3

Math Help - irritating differential equation

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    4

    irritating differential equation

    hey guys, im having extreme difficulties with this question, mostly trying to figure out exactly what the question is asking, if you could give any help it would be appreciated.


    The differential equation governing the angle theta
    subtended by a spherical pendulum with
    the downward vertical is:

    d^2theta/dt^2 - x = 2cost



    (a) The period of a spherical pendulum is given by the complete elliptic integral of the first kind K, which is

    K(m) = integral of dtheta/sqrt(1-m*sintheta^2) in the intervals of pi/2 and 0


    Take m = 0:5 and use the Trapezoidal rule with step sizes pi/8 and pi/16 to estimate

    K
    (0.5). Then use Richardson extrapolation to obtain an improved estimate for

    K
    (0.5).
    (b) Assume that the pendulum has been set in motion from the vertical with angular
    velocity 1, so that theta
    = 0 and dtheta/dt = 1 at t = 0. Show that the subsequent motion of the pendulum can be found by solving the differential equation

    dtheta/dt = sqrt(2costheta-1)

    with theta = 0 at t = 0 use euler's method with step size delta(t) = 0.1 to estimate 0.3


    dtod with step size t = 0:1 to estimate (0:3).


    If any1 could also tell me how to write out these equations properly, tht would be very handy indeed

    Many thanks,
    dumbguy321
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dumbguy321 View Post
    hey guys, im having extreme difficulties with this question, mostly trying to figure out exactly what the question is asking, if you could give any help it would be appreciated.




    The differential equation governing the angle theta
    subtended by a spherical pendulum with
    the downward vertical is:

    d^2theta/dt^2 - x = 2cost


    (a) The period of a spherical pendulum is given by the complete elliptic integral of the first kind K, which is

    K(m) = integral of dtheta/sqrt(1-m*sintheta^2) in the intervals of pi/2 and 0


    Take m = 0:5 and use the Trapezoidal rule with step sizes pi/8 and pi/16 to estimate
    K


    (0.5). Then use Richardson extrapolation to obtain an improved estimate for
    K


    (0.5).
    (b) Assume that the pendulum has been set in motion from the vertical with angular
    velocity 1, so that theta

    = 0 and dtheta/dt = 1 at t = 0. Show that the subsequent motion of the pendulum can be found by solving the differential equation

    dtheta/dt = sqrt(2costheta-1)

    with theta = 0 at t = 0 use euler's method with step size delta(t) = 0.1 to estimate 0.3



    dtod with step size t = 0:1 to estimate (0:3).


    If any1 could also tell me how to write out these equations properly, tht would be very handy indeed

    Many thanks,
    dumbguy321

    Some clarifications have been established in this thread: http://www.mathhelpforum.com/math-he...-equation.html

    I don't have time to say more at the moment.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    4
    sorry for posting twice. This question is for my homework tmoro, I'd posted it in the differential equations file and I thought I wouldnt get fast enough reply.
    Anyway im sorry, thanks for ur time, I'v figured how to do the question now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. irritating derivative problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 19th 2011, 05:25 PM
  2. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  3. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  4. Irritating probability question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 3rd 2010, 10:42 AM
  5. Replies: 3
    Last Post: May 25th 2010, 12:01 AM

Search Tags


/mathhelpforum @mathhelpforum