# Spring pendulum system fortran program

• Comp Sci
I just want to know if someone has the fortran code for the numerical solution of the pendulum with a spring. And if it is so, can it write it here?

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I just want to know if someone has the fortran code for the numerical solution of the pendulum with a spring. And if it is so, can it write it here?

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Ok, this is what I have:

PROGRAM DIFFERENTIAL_EQUATIONS_SYSTEM

WRITE (*,*) 'WRITE A, B, N, ALF1 AND ALF2'
H=(B-A)/N
T=A
W1=ALF1
W2=ALF2

OPEN(10,FILE='RUNGE_KUTTA_HIGHER_ORDER.TXT')

DO I=1,N

WRITE (10,*) T,W2
WRITE (*,*) T,W2

W1=W1+H*F1(T,W1,W2)
W2=W2+H*F2(T,W1,W2)
T=A+I*H

END DO
END

FUNCTION F1(T,W1,W2)
REAL W1,W2,T
F1=W1
RETURN
END

FUNCTION F2(T,W1,W2)
REAL W1,W2,T
F2=-3.0*W2-(9.8/3.0)*SIN(W1)
RETURN
END

maybe my way of programming is not the best. What I have are the equations of motion for the pendulum-spring system, they are coupled, and I don't know how to solve them numerically, any help???

And it would be any advice to improve my programming it is welcomed.

Could you please explain a bit more about the problem and your code? When you say pendulum-spring system, do you mean a rigid pendulum with a mass on the end is hanging from a spring? Can you show us the equations of motion you're using? And what method are you trying to use, 2nd-order Runge-Kutta?

As for the variables, I'm guessing A and B are initial and final times, N is number of timesteps, ALF1 and ALF2 are initial angles of the spring and pendulum, respectively. Correct? More descriptive variable names in general are very helpful if anyone besides yourself needs to understand your code.

A Fortran tip you may not be aware of: declare your variables explicity everywhere (like how you did in your functions: REAL W1,W2,T), and put IMPLICIT NONE as the first line in all of your programs and functions/subroutines, which forces you to declare your varibles. If you do not explicity declare varibles, Fortran implicity does so in the following manner. If the first letter of your variable name is I, J, K, L, M or N, it will be an INTEGER, otherwise it will be a REAL. This is widely considered to be one of the worst features of Fortran, and using IMPLICIT NONE is always recommended. In your code there are no problems with this, but it's easy to make mistakes.

Could you please explain a bit more about the problem and your code? When you say pendulum-spring system, do you mean a rigid pendulum with a mass on the end is hanging from a spring? Can you show us the equations of motion you're using? And what method are you trying to use, 2nd-order Runge-Kutta?
The theory is on the pages 42-43 of the book.pdf file. I made a mistake with the name of the code, the method it isn't Runge-Kutta it is Euler's Method but for a second order differential equation.

All you assume on second paragraph it is right, about the variables. And thanks for the tip, I will keep it in mind.

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You'll have to introduce some phase/state variables to convert those two 2nd-order ODEs into four 1st-order ODEs, and then solve those. http://12000.org/my_courses/UC_davis/spring_2011/MAE_121_eng_dynamics/lab/lab_one/report/report.htm" [Broken] (eqn 3 and the ones above it). Hope that helps.

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