Excel - help with eulers method on coupled equations

[ragga puffin]

im doing a simulation on a magnetic moment in a magnetic field B and I am quite stuck.

its a set of coupled equations: m'-x=B*m-y & m'-y= - B*m-x
where m-x is the x component, ' is rate of with respect to time etc.
the vector should be precessing in a circle with frequency w= - B, B is set to one so it should make one rotation in one second -> full cycle -> full sine wave, but i seem to only be getting about half a sine wave

the cosine term in the m'-y formula can be neglected, as can the m'-z and m-z columns because the starting point is M'= M X B (the cross product of the moment and the magnetic field) and B is defined as being in the z direction.

im pretty sure the equations are right and the problem lies in my formulae in excel, any help will be greatly appreciated:!)

 

[berkeman]

I filled the data for mx down past 1.5 seconds and plotted it, and it looks reasonable except for the expected period that you mention. How did you derive that the period should be 1? Is there maybe a factor of PI missing? It looks like the period is actually closer to PI...

 

[oswaler]

First of all, it's great that you are using Excel for your simulation. It can be a powerful tool for solving complex equations. In order to troubleshoot the issue, I would recommend checking your initial conditions and the values of your parameters. Make sure that your initial values for m-x and m-y are correct and that your value for B is set to 1, as you mentioned. It's also important to double check your equations and make sure that you are using the correct variables in your spreadsheet.

Another potential issue could be the step size that you are using in your Euler's method. If the step size is too large, it can lead to inaccurate results. I would suggest trying different step sizes and seeing if that makes a difference in your simulation.

Additionally, it may be helpful to plot your results and compare them to what you expect to see. This can help you identify where the issue may be occurring. You can also try using a different numerical method, such as the Runge-Kutta method, to see if that gives you better results.

If you are still having trouble, I would suggest seeking assistance from a colleague or a professor who has experience with numerical methods and simulations. They may be able to provide additional insights and help you troubleshoot the issue.

Overall, it's important to carefully check your equations, initial conditions, and parameters to ensure that everything is correct. With some trial and error and perhaps some assistance, I'm confident that you will be able to solve the issue and get accurate results for your simulation. Good luck!