import numpy as np 

def pseudo_potential_approximation(t, omega_rf, q, beta):
    return np.cos(0.5*beta*omega_rf*t)*(1 - 0.5*q*np.cos(omega_rf*t))

def mathieu_ode(u, t, a, q):
    return (u[1], u[0]*(2*q*np.cos(2*t) - a))
84f0a043372d31d1f4d44efa31403e5a37a90cf3
<mask token>

<mask token>


def mathieu_ode(u, t, a, q):
    return u[1], u[0] * (2 * q * np.cos(2 * t) - a)

<mask token>


def pseudo_potential_approximation(t, omega_rf, q, beta):
    return np.cos(0.5 * beta * omega_rf * t) * (1 - 0.5 * q * np.cos(
        omega_rf * t))


def mathieu_ode(u, t, a, q):
    return u[1], u[0] * (2 * q * np.cos(2 * t) - a)

import numpy as np


def pseudo_potential_approximation(t, omega_rf, q, beta):
    return np.cos(0.5 * beta * omega_rf * t) * (1 - 0.5 * q * np.cos(
        omega_rf * t))


def mathieu_ode(u, t, a, q):
    return u[1], u[0] * (2 * q * np.cos(2 * t) - a)

import numpy as np 

def pseudo_potential_approximation(t, omega_rf, q, beta):
    return np.cos(0.5*beta*omega_rf*t)*(1 - 0.5*q*np.cos(omega_rf*t))

def mathieu_ode(u, t, a, q):
    return (u[1], u[0]*(2*q*np.cos(2*t) - a))