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Proyecto Pendulo/600_G.py

+import math
+import numpy as np
+import matplotlib.pyplot as plt
+
+def integral(k, theta):
+    def integrando(t):
+        return 1 / math.sqrt(1 - k**2 * math.sin(t)**2)
+    
+    puntos = 1000
+    h = (theta - 0) / puntos
+    sumadelaintegral = 0.0
+    
+    for i in range(puntos + 1):
+        t = i * h
+        weight = 2 if i == 0 or i == puntos else 4 if i % 2 == 1 else 2
+        sumadelaintegral += weight * integrando(t)
+    
+    return (h / 3) * sumadelaintegral
+
+def periodo(L, g, theta):
+    alpha = theta / 2
+    k = math.sin(alpha)
+    T = 4 * math.sqrt(L / g) * integral(k, math.pi/2)
+    return T
+
+longitudpendulo = 1.0
+aceleraciongravedad = 9.81
+anguloinicialengrados = 17.12
+
+anguloinicialenradianes = math.radians(anguloinicialengrados)
+periodo_calculado = periodo(longitudpendulo, aceleraciongravedad, anguloinicialenradianes)
+
+def movimiento_pendulo(tiempo, L, g, angulo_inicial):
+    alpha = angulo_inicial / 2
+    k = math.sin(math.radians(alpha))
+    T = periodo(L, g, math.radians(angulo_inicial))
+    omega = 2 * math.pi / T
+
+    theta = math.radians(angulo_inicial)
+    omega_t = 0.0
+
+    angulos = []
+    tiempos = []
+
+    for t in tiempo:
+        angulos.append(math.degrees(theta))
+        tiempos.append(t)
+        
+        alpha = theta / 2
+        k = math.sin(alpha)
+        omega_t = omega_t + (-g / L) * math.sin(theta) * (T / len(tiempo))
+        theta = theta + omega_t * (T / len(tiempo))
+
+    return tiempos, angulos
+
+tiempo_inicial = 0.0
+tiempo_final = 5.0
+numero_puntos = 1000
+tiempo = np.linspace(tiempo_inicial, tiempo_final, numero_puntos)
+
+# --------Datos medidos con Tracker-----------------
+tiempo_medido = [0.000, 0.017, 0.033, 0.050, 0.067, 0.083, 0.100, 0.117, 0.133, 0.150, 0.167, 0.183, 0.200, 0.217, 0.234, 0.250, 0.267, 0.284, 0.300, 0.317, 0.334, 0.350, 0.367, 0.384, 0.400, 0.417, 0.434, 0.450, 0.467, 0.484, 0.500, 0.517, 0.534, 0.550, 0.567, 0.584, 0.600, 0.617, 0.634, 0.651, 0.667, 0.684, 0.701, 0.717, 0.734, 0.751, 0.767, 0.784, 0.801, 0.817, 0.834, 0.851, 0.867, 0.884, 0.901, 0.917, 0.934, 0.951, 0.967, 0.984, 1.001, 1.017, 1.034, 1.051, 1.068, 1.084, 1.101, 1.118, 1.134, 1.151, 1.168, 1.184, 1.201, 1.218, 1.234, 1.251, 1.268, 1.284, 1.301, 1.318, 1.334, 1.351, 1.368, 1.384, 1.401, 1.418, 1.434, 1.451, 1.468, 1.484, 1.501, 1.518, 1.535, 1.551, 1.568, 1.585, 1.601, 1.618, 1.635, 1.651, 1.668, 1.685, 1.701, 1.718, 1.735, 1.751, 1.768, 1.785, 1.801, 1.818, 1.835, 1.851, 1.868, 1.885, 1.901, 1.918, 1.935, 1.952, 1.968, 1.985, 2.002, 2.018, 2.035, 2.052, 2.068]
+
+angulo_medido = [17.12, 16.78, 16.41, 15.98, 15.57, 14.94, 14.31, 13.80, 13.40, 12.94, 12.50, 12.11, 11.54, 11.04, 10.50, 10.05, 9.274, 8.667, 8.150, 7.351, 6.653, 5.881, 5.203, 4.492, 3.810, 3.077, 2.320, 1.607, 0.867, 0.160, -0.619, -1.286, -1.957, -2.651, -3.288, -3.884, -4.470, -5.035, -5.574, -6.140, -6.558, -6.999, -7.213, -7.891, -8.296, -8.914, -9.307, -9.706, -10.03, -10.29, -10.51, -10.70, -10.83, -11.03, -11.15, -11.34, -11.54, -11.61, -11.80, -11.94, -11.97, -11.97, -11.82, -11.76, -11.56, -11.33, -11.03, -10.70, -10.40, -10.07, -9.656, -9.304, -8.912, -8.493, -8.069, -7.665, -7.028, -6.616, -5.951, -5.424, -4.855, -4.241, -3.628, -2.983, -2.298, -1.593, -0.916, -0.185, 0.534, 1.295, 2.086, 2.754, 3.465, 4.127, 4.718, 5.338, 6.001, 6.645, 7.197, 7.801, 8.537, 9.064, 9.860, 10.51, 11.53, 12.10, 12.73, 13.08, 13.66, 13.95, 14.44, 14.86, 15.06, 15.50, 15.74, 15.99, 16.26, 16.49, 16.69, 16.91, 17.09, 17.24, 17.30, 17.35, 17.36]
+
+tiempo_medido_arr = np.array(tiempo_medido)
+angulo_medido_arr = np.array(angulo_medido)
+
+tiempos_simulados, angulos_simulados = movimiento_pendulo(tiempo_medido_arr, longitudpendulo, aceleraciongravedad, anguloinicialengrados)
+
+#-----------------Gráfica--------------------
+plt.plot(tiempo_medido, angulo_medido, 'bo', label='Datos medidos')
+plt.plot(tiempos_simulados, angulos_simulados, 'r-', label='Simulación')
+plt.xlabel('Tiempo (s)')
+plt.ylabel('Ángulo (grados)')
+plt.title('Comparación Datos Medidos y Simulación del Péndulo')
+plt.legend()
+plt.grid(True)
+plt.show()
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