// Appendix D.1 (p121) of Klein and Godunov Introductory Computational Physics
// program to calculate the mass on a spring problem.
//m=k=1; therefore a=-x
//with the simple Euler method
//ak 9/7/00
//all in double precision
//small adjustments isv Jan. 2017
#include <iostream>
#include <fstream>
#include <math.h>
#include <iomanip>
#include <stdio.h>
using namespace std;


int main (int argc, char **argv)
{
   int n=100; // number of steps
   double v[n+1]; //the forward value calculated
   double vinit= 5.;// initial velocity
   double x[n+1];// the forward x-value
   double xinit= 0.;// initial position
   double energy[n+1]; // the energy from mv**2/2+kx**2/2
   double ti[n+1];//the array of times
   double step=0.1; //the step size for the euler method
   double time=0.;; //the time

   int i = 0;//the loop counter
// initial conditions
   ti[i]=time;
   v[i]=vinit;
   x[i]=xinit;
   energy[i]=0.5*xinit*xinit + 0.5*vinit*vinit;
   cout << ti[i] << " " << x[i] << " " << v[i] << " " << energy[i] << endl;

   while(i < n)  //make n steps
      {
      v[i+1]=v[i]-step*x[i]; //calculate the forward velocity
      x[i+1]=x[i]+step*v[i]; //calculate the forward position
      energy[i+1]=pow(x[i+1],2)/2.+pow(v[i+1],2)/2.; //energy conservation
      time=time+step;
      ti[i+1]=time;
      i=i+1;
      cout << ti[i] << " " << x[i] << " " << v[i] << " " << energy[i] << endl;
      }
}