.:: Spring Mass Fourier Transform ::.
Fourier Transform using Spring Mass System
This is a fourier transform demo based on the concept of tuning forks and sping mass systems. A spring and a mass have a resonance frequency. By feeding an analog signal to a set of springs and masses you will see some of them resonate. By measuring their average velocity, you can determine the frequencies in a signal.
SOFTWARE WRITTEN IN C#
1: using System;
2: using System.Collections.Generic;
3: using System.Linq;
4: using System.Text;
5: using System.Threading;
6:
7: namespace ConsoleApplication1
8: {
9: class Program
10: {
11: static void Main(string[] args)
12: {
13: while (true)
14: {
15: int n = 10;
16: double[] k = new double[] {1,8,15,22,29,36,43,50,57,64};
17: double[] m = new double[] {1,1,1,1,1,1,1,1,1,1};
18: double[] x = new double[n];
19: double[] vx = new double[n];
20: double[] ax = new double[n];
21: double dt = .1;
22: double t = 0;
23:
24: double[] av = new double[n];
25: int avcounter = 0;
26:
27: for (int i = 0; i < n; i++)
28: {
29: x[i] = 0;
30: vx[i] = 0;
31: ax[i] = 0;
32: }
33:
34: //clear average
35: for (int i = 0; i < n; i++)
36: {
37: av[i] = 0;
38: }
39:
40: //get sine wave frequency
41: Console.Write("Frequency (1 to 100): ");
42: double sinfreq = Convert.ToDouble(Console.ReadLine());
43:
44: while (t < 10)
45: {
46: for (int i = 0; i < n; i++)
47: {
48: ax[i] = (forcefunction(t,sinfreq) + (-x[i] * k[i])) / m[i];
49: vx[i] += 2 * ax[i] * dt;
50: x[i] += 2 * vx[i] * dt;
51: }
52: t += dt;
53:
54: //count averages
55: avcounter++;
56: for (int i = 0; i < n; i++)
57: {
58: av[i] += Math.Abs(vx[i]);
59: }
60:
61: //draw
62: Console.Clear();
63: DisplayMass(x[0], m[0], k[0]);
64: DisplayMass(x[1], m[1], k[1]);
65: DisplayMass(x[2], m[2], k[2]);
66: DisplayMass(x[3], m[3], k[3]);
67: DisplayMass(x[4], m[4], k[4]);
68: DisplayMass(x[5], m[5], k[5]);
69: DisplayMass(x[6], m[6], k[6]);
70: DisplayMass(x[7], m[7], k[7]);
71: DisplayMass(x[8], m[8], k[8]);
72: DisplayMass(x[9], m[9], k[9]);
73: Console.WriteLine();
74: DisplayMass(forcefunction(t,sinfreq), 0, 0);
75: Thread.Sleep(50);
76: }
77:
78: //count averages
79: Console.WriteLine();
80: for (int i = 0; i < n; i++)
81: {
82: av[i] /= avcounter;
83: Console.WriteLine(av[i] + " m/s");
84: }
85: Console.WriteLine("Loops: " + avcounter.ToString());
86: }
87: }
88:
89: public static double forcefunction(double t, double f)
90: {
91: return (Math.Sin(t / (2 * Math.PI) * f));
92: }
93: public static void DisplayMass(double x,double m, double k)
94: {
95: string buff = "freq: " + String.Format("{0:0.00}", Math.Sqrt(k / m)) + " mass: " + m.ToString() + " k: " + k.ToString() + " [";
96: int num = (int)Math.Floor(10 * x)+10;
97: for (int i = 0; i < num; i++)
98: {
99: buff += "X";
100: }
101: buff += "X";
102: Console.WriteLine(buff);
103: }
104: }
105: }