Algoritmo de Velocidade de Verlet (osc. forçado amortecido)

#include <stdio.h>
#include <math.h>

#define x0 2.0

#define v0 1.0

#define t0 0.0
#define tf 100.0

#define w02 3.0
#define w0 (sqrt(w02))
#define xi 1.1
#define F0m 0
#define omega w0*sqrt(1-0.2)

#define dt 1e-2
#define N ((tf-t0)/dt)

double phi(double x, double t, double v)
{
    return -w02*x + F0m*sin(omega*t) - 2*xi*v*w0;
}

double E(double x, double v)
{
    return v*v/w02 + x*x;
}

int main(void)
{
    double x = x0, xn,
           t = t0, tn,
           v = v0, vn;

    FILE *h = fopen("./diferencial.dat","w+");

    double E0 = E(x,v);

    for (int i = 0; i < N; ++i)
    {
        tn = t + dt;
        xn = x + vn*dt + 0.5*phi(x,t,v)*dt*dt;
        vn = v + 0.5*(phi(xn,tn,v)+phi(x,t,v))*dt;

        fprintf(h, "%d %f %f %f\n", i, t, x, E(x,v)/E0-1);

        t = tn;
        x = xn;
        v = vn;
    }

    fclose(h);
    return 0;
}