.:: 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: }