Results 1 to 7 of 7

Math Help - Problem with differential equation

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    4

    Problem with differential equation

    Hello people I have a problem with this exercise.
    I need to show that a motion of a pendulum can be found by solving the differential equation
    dx/dt=sqrt(2cosx-1) with x=0 at t=0

    The problem arises when I try to rearrange the equation and calculate the integral of dx/sqrt(2cosx-1) which brings me nowhere. Anyone has any idea on how to solve this differential equation?
    Also, I can't do the next part of the question, which is using Eulers method with t=0.1 to estimate x(0.3) if I don't find first a solution to the equation.

    Any help would be greatly appreciated
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by yvchi View Post
    Hello people I have a problem with this exercise.
    I need to show that a motion of a pendulum can be found by solving the differential equation
    dx/dt=sqrt(2cosx-1) with x=0 at t=0

    The problem arises when I try to rearrange the equation and calculate the integral of dx/sqrt(2cosx-1) which brings me nowhere. Anyone has any idea on how to solve this differential equation?
    Also, I can't do the next part of the question, which is using Eulers method with t=0.1 to estimate x(0.3) if I don't find first a solution to the equation.

    Any help would be greatly appreciated
    It looks like it is not expressible in terms of basic functions ^^'
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by yvchi View Post
    Hello people I have a problem with this exercise.
    I need to show that a motion of a pendulum can be found by solving the differential equation
    dx/dt=sqrt(2cosx-1) with x=0 at t=0

    The problem arises when I try to rearrange the equation and calculate the integral of dx/sqrt(2cosx-1) which brings me nowhere. Anyone has any idea on how to solve this differential equation?
    Also, I can't do the next part of the question, which is using Eulers method with t=0.1 to estimate x(0.3) if I don't find first a solution to the equation.

    Any help would be greatly appreciated
    Do you need to solve the differential equation or just show that the motion satisfies this differential equation. There's a big difference between these two things!

    As for using Eulers Method .... you don't need to have solved the differential equation in order to apply this method! It is a method for getting a numerical approximation to a solution.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2009
    Posts
    4
    Well, the question asks to show that the motion satisfies this differential equation, but how else am I supposed to show it if I don't solve it??
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by yvchi View Post
    Well, the question asks to show that the motion satisfies this differential equation, but how else am I supposed to show it if I don't solve it??
    You construct the differential equation from first principles, starting with a force diagram.

    You will find this stuff in most textbooks dedicated to Classical Mechanics.

    By the way, what's x meant to represent? And is the pendulem meant to be a simple pendulem?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Feb 2009
    Posts
    4
    the question is about a spherical pendulum which has an equation of d^2x/dt^2 +sinx=0. It then tells you to assume that the pendulum is set in motion from the vertical with angular velocity 1 so that x=0 and dx/dt=1 at t=0. It then asks to show that the subsequent motion can be found by solving the differential eqn i posted earlier.

    And I just used x instead of angle theta so x should be an angular quantity
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by yvchi View Post
    Hello people I have a problem with this exercise.
    I need to show that a motion of a pendulum can be found by solving the differential equation
    dx/dt=sqrt(2cosx-1) with x=0 at t=0

    The problem arises when I try to rearrange the equation and calculate the integral of dx/sqrt(2cosx-1) which brings me nowhere. Anyone has any idea on how to solve this differential equation?
    Also, I can't do the next part of the question, which is using Eulers method with t=0.1 to estimate x(0.3) if I don't find first a solution to the equation.

    Any help would be greatly appreciated
    The complete question has been asked by another user here: http://www.mathhelpforum.com/math-he...-equation.html

    Thread closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 11th 2011, 02:17 AM
  2. differential equation problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 7th 2010, 12:21 PM
  3. Differential Equation Problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 26th 2010, 03:49 PM
  4. differential equation problem
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: February 20th 2009, 03:01 AM
  5. Problem with a differential equation
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 29th 2008, 02:11 PM

Search Tags


/mathhelpforum @mathhelpforum