import numpy as np
import matplotlib.pyplot as plt



m = 0.05
x0 = 0.5E-2
k = 4.5
omega = np.sqrt(k/m)
t = np.linspace(0, 20, 1000)
x = x0 * np.sin(omega*t)
v = x0 * omega * np.cos(omega*t)
a = -x0 * omega**2 * np.sin(omega*t)


fig, ax = plt.subplots(3, 1, sharex = True)
ax[0].set_title("Mouvement d'un pendule simple: m = %.3f g, $x_0$ = %.2f cm, k = %.2f N/m" %(m*1000, x0*100, k))
ax[0].plot(t, x, 'r')
ax[0].set_ylabel("Position (m)")
ax[0].set_xlim([np.min(t), np.max(t)])
ax[0].set_ylim([-1.2 * np.max(x), 1.2 * np.max(x)])
#ax[0].grid()

ax[1].plot(t, v, 'g')
ax[1].set_ylabel("Vitesse (m/s)")
ax[1].set_xlim([np.min(t), np.max(t)])
ax[1].set_ylim([-1.2 * np.max(v), 1.2 * np.max(v)])
ax[1].grid()

ax[2].plot(t, a, 'b')
ax[2].set_xlabel('Temps(s)')
ax[2].set_ylabel("Accélération (m/s²)")
ax[2].set_xlim([np.min(t), np.max(t)])
ax[2].set_ylim([-1.2 * np.max(a), 1.2 * np.max(a)])
ax[2].grid()

plt.figure()
plt.title("Espace des phases")
plt.plot(x, v, "m")
plt.ylabel("Vitesse")
plt.xlabel("Position")
plt.axis("equal")

plt.show()