# Problem with differential equation

• Feb 21st 2009, 12:34 PM
yvchi
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
\$\displaystyle 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 \$\displaystyle 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
• Feb 22nd 2009, 12:37 AM
Moo
Hello,
Quote:

Originally Posted by yvchi
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
\$\displaystyle 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 \$\displaystyle 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 ^^'
• Feb 22nd 2009, 01:53 AM
mr fantastic
Quote:

Originally Posted by yvchi
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
\$\displaystyle 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 \$\displaystyle 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.
• Feb 22nd 2009, 03:14 AM
yvchi
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??
• Feb 22nd 2009, 04:11 AM
mr fantastic
Quote:

Originally Posted by yvchi
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?
• Feb 22nd 2009, 04:52 AM
yvchi
the question is about a spherical pendulum which has an equation of \$\displaystyle 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
• Feb 22nd 2009, 03:58 PM
mr fantastic
Quote:

Originally Posted by yvchi
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
\$\displaystyle 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 \$\displaystyle 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