Results 1 to 5 of 5

Math Help - A pendulum question

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Britain
    Posts
    9

    A pendulum question

    A pendulum question-image.jpgA pendulum question-image.jpgA pendulum question-image.jpg

    Hello I have included pictures of the question I would like some help with and also the solution I have been given. I am fine up until part c. However I really do not understand how to do any part of c. So if there is anyone out there who thinks they could make it easier to understand your help would be really appreciated.

    Thank you
    Attached Thumbnails Attached Thumbnails A pendulum question-image.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1

    Re: A pendulum question

    I guess the real question is do you know how to solve the differential equation? The rest of the solution is based entirely on that.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Britain
    Posts
    9

    Re: A pendulum question

    The problem is I do not understand where they have got those equations from.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,095
    Thanks
    317

    Re: A pendulum question

    If you understand part B then you understand the derivation of the differential equation:

     \ddot \theta + 2 \lambda \dot \theta + \omega^2 \theta = 0

    In Part C they have simply substituted  \theta = e^{\alpha t}:

     \frac {d^2(e^{\alpha t})}{dt^2} + 2 \lambda \frac {d(e^{\alpha t})}{dt} + \omega^2 e^{\alpha t} = 0

    Do the differentiation and you get

     \alpha^2 e^{\alpha t} + 2 \lambda \alpha e^{\alpha t} + \omega^2 e^{\alpha t}=0

    Now divide through by  e^{\alpha t} and you get their equation:

     \alpha^2 + 2 \lambda \alpha + \omega^2 = 0


    Is this helpful in getting you started in part C?
    Last edited by ebaines; April 25th 2013 at 11:38 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2012
    From
    Britain
    Posts
    9

    Re: A pendulum question

    Thank you! That is very helpful.
    Firstly where did they get that substitution from?
    Also how did they find the equation for theta in part i of C?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Length of pendulum
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: June 13th 2009, 04:03 AM
  2. Trig. pendulum question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: June 11th 2008, 09:23 PM
  3. pendulum
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 12th 2008, 06:21 PM
  4. pendulum
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: March 1st 2008, 07:56 PM
  5. Pendulum
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 30th 2005, 04:05 AM

Search Tags


/mathhelpforum @mathhelpforum