def METHOD_NAME():
    global x, xprev, t, n
    ret_x = []
    ret_xdot = []
    for _ in range(timesteps_per_update):
        xnext = (2*beta*x + (alpha - beta)*xprev - dV_dx(x) + gamma*np.cos(omega*t)) / (alpha+beta)
        n += 1
        t += dt
        xdot = (xnext - xprev) / (2*dt)
        xprev = x
        x = xnext
        if n % timesteps_per_plot == 0:
            ret_x.append(x)
            ret_xdot.append(xdot)
    return ret_x, ret_xdot