// program to calculate the mass on a spring problem.
// m=k=1; therfore a=-x
// with the simple euler method
// ak 9/7/00
// all in double precision
#include <iostream.h>
#include <fstream.h>
#include <math.h>
#include <iomanip.h>
#include <stdio.h>
#include "TROOT.h"
#include "TApplication.h"
#include "TCanvas.h"
#include "TLine.h"
#include "TFile.h"
#include "TGraph.h"
 TROOT root("hello","Spring Problem"); // initalize root
int main(int argc, char **argv)

 {
	double v_new[100]; // the forward value calculated
	double v_old=5.; // the previous value; for the first calculation
			 // the boundary condition
	double x_new[100]; // the forward x-value
	double x_old=0.;// the x value from previous
	double energy[100]; // the energy from mv**2/2+ kx**2/2
	double ti[100]; //array to hold the time
	double step =0.1; // the step size for the euler method
	double time=0. ;// the time

	int loop = 0;	// the loop counter

	// first the root stuff
   	TApplication theApp("App", &argc, argv);
	
	TCanvas *c = new TCanvas("c", "Hyperbola", 600, 600); //* create Canvas

	TFile *out_file = new TFile("spring.root","RECREATE","sping"); // create root
								//file
	
	// create the graphs //

	
	while (loop <100)
		{
		v_new[loop]=v_old-step*x_old; // calculate the forward velocity
		x_new[loop]=x_old+step*v_old; // calculate the forward position
		energy[loop]=pow(x_new[loop],2)/2+pow(v_new[loop],2)/2.; // energy conservation
		energy[loop]=energy[loop]/5. ;// rescaled for plotting purposes
		

		time=time+step;	// move forward in time by the step
		v_old=v_new[loop];	// the new value becomes now the old
		x_old=x_new[loop];
		ti[loop]=time;
		time=time+step;	// move forward in time by the step
		loop=loop+1;
		}
		
	TGraph *root1 = new TGraph(100,ti,x_new);
	TGraph *root2 = new TGraph(100,ti,v_new);
	TGraph *root3 = new TGraph(100,ti,energy);
		root1->SetTitle("Spring with simple Euler Method");
		
		root1->SetLineColor(1);
		root1->Draw("AC");
		root1->Write();
		root2->SetLineWidth(2);
		root2->SetLineColor(2);
		root2->Draw("C");
		root2->Write();
		root2->SetLineWidth(2);
		root3->SetLineColor(4);
		root3->Draw("C");
		root3->Write();
		
		// put everyhting into the file
		out_file->Write();
		out_file->Close();

	  theApp.Run();
	
	}
	
// compile g++ -o spring spring.cxx wit root libraries