Plotting data from simulation of springs with masses

Questions
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1

Below I have code for springs with masses attached to them. How can I plot it so that the position (X) is on the vertical axis and time (T) is on the horizontal axis?

kp = 40; (* Spring constant *)
kc = 250;(* Spring constant *)
deltaT = .03; (* Time Step *)
m = 1; (* Mass *)

iini = 0;
ilast = 25;
nini = 0;
nlast = 300;


X = 0;
V = .01;
F = 50;
T[nini] = 0;



For[i = iini, i <= ilast, i++,

  For[n = nini, n <= nlast, n++'

      X[i + 1] = X[i] + V[i]*deltaT;

    T[n + 1] = T[n] + deltaT;

    V[i + 1]  =   
     V[i] -   (kc (X[i + 1] + X[i - 1] - 2*X[i] + 
            kp (V[i]*T[n + 1] - X[i]) + F[i])/m)*deltaT;
    ];
  ];
2

Hello Sean,

I am not that good at physics, so I apologies if my idea does to fit to the purpose.

I would suggest loosing the “For” loop. It is my experience with Mathematica, that whenever you use loops, there is a more clean way of doing things. In your case, I might consider using Recurrence Table, and then merge the lists using Transpose. Then you can plot the data via ListPlot. :slight_smile:

For instance:

kp = 40;(*Spring constant*)
kc = 250;(*Spring constant*)

deltaT = .03;(*Time Step*)
m = 1;(*Mass*)

iini = 0;
ilast = 25;
nini = 0;
nlast = 300;

X = 0;
V = .01;
F = 50;
T = 0;

lstTime = 
  RecurrenceTable[{time[n + 1] == time[n] + deltaT, time[1] == nini}, 
   time, {n, nini + 1, nlast}];

Hope it helps, or that someone can help you with a better answer :slight_smile:

Edit: As I am sure you recognized, I left out writing the “V[n+1]”. Simply because I fear I would write the expression wrong when I do not know the physics behind it in detail. So it is for you to fill out :slight_smile:

Edit 2: I completely forgot to say that RecurrenceTable allows for more systems of equations than just a single one. In which case you will not need to Transpose prior plotting, I presume. Check out http://reference.wolfram.com/mathematica/ref/RecurrenceTable.html.

3

Hi Sean,
It seems you are trying to solve some diffferential equations. Mathematica can do this directly using the DSolve function (for exact solutions), or the NDSolve function (for numerical solutions).

4

Sean,

you can visualize data of type {{t0, x0}, {t1, x1}, {t2, x2}, …} with ListPlot, see

http://reference.wolfram.com/mathematica/ref/ListPlot.html

The function or interpolation function you would get from Nick’s suggestion can be visualized with Plot:

http://reference.wolfram.com/mathematica/ref/Plot.html

If you are not required to use any particular numerical method then I would also strongly recommend you to use either DSolve or NDSolve to find your answer. Hope this helps.

5

I would recommend looking through numerous Demonstrations we have - there are quite a few on spring and mass system simulations. The Mathematica code is freely available for download - that could be your starting point.