Numerical integration of an harmonic oscillator using java

[user123897]

Hi, I am trying to analyze the an harmonic oscillator using kinematics.
first i calculate the force applied by the spring (f = (-x)*k)
then i calculate the acceleration (a = f/m)
then speed (v= v0 + v0t + 0.5*a*t^2)
and finally update x (x = x0+vt)

this is a simplfied loop of my program (written in java, all values are initialized to 0 expect x = 10)

{
x = x + v * dt + 0.5 * a * Math.pow(dt, 2);
f = k * (-x);
a = ((f / m) + a) / 2;
v = v + a * dt;
a = f / m;
}

this loop runs evry dt milliseconds.

the values of x,v,a,f increase rapidly and aims to infinitey

can someone understand where i got it wrong?

thanks for your time :)

 

[BvU]

a = ((f / m) + a) / 2;

what's this ?

 

[user123897]

what's this ?

average acceleration. note that the a in the right side is the previous acceleration.

 

[QuantumQuest]

can someone understand where i got it wrong?

What kind of loop is this (for, while...) and where are the condition(s) of it, especially the one (or whatever combination), that stop the loop from running indefinitely? From what function do you get dt to count?

 

[BvU]

average acceleration. note that the a in the right side is the previous acceleration.

I see. It's not he problem, though. In fact I can't reproduce your runaway:

 

[user123897]

I see. It's not he problem, though. In fact I can't reproduce your runaway:

View attachment 104489

Figured out the problem. I dt = 10, way too big considering the expected period time.

Thanks for your help!

 

[BvU]

10 milliseconds isn't bad. 10 seconds is.

 

[vanhees71]

The main problem is using Java for numerics, I guess ;-)). SCNR.

 

[BvU]

Real programmers can write Fortran in any language.