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Proyecto Pendulo/codigo_300_C.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 = 3.407
+
+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, 0.650, 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, 1.067, 1.084, 1.101, 1.117, 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, 1.534, 1.551, 1.568, 1.584, 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, 1.951, 1.968, 1.985, 2.001, 2.018, 2.035, 2.052, 2.068]
+
+angulo_medido = [3.407, 3.283, 3.177, 3.083, 3.005, 2.548, 2.951, 2.499, 2.846, 2.755, 2.193, 2.026, 1.838, 2.125, 1.577, 1.498, 1.837, 1.750, 1.633, 1.498, 1.310, 1.108, 0.939, 0.761, 0.623, 0.520, 0.423, 0.308, 0.200, 2.808E-2, -0.147, -0.373, -0.570, -1.155, -1.286, -1.390, -1.459, -1.564, -1.671, -1.804, -1.968, -2.133, -2.292, -2.419, -2.512, -2.576, -2.623, -2.666, -2.733, -2.820, -2.913, -3.012, -3.095, -3.157, -3.179, -3.170, -3.148, -3.133, -3.129, -3.145, -3.167, -3.203, -3.214, -3.209, -3.149, -3.067, -2.965, -2.855, -2.791, -2.721, -2.673, -2.626, -2.562, -2.482, -2.364, -2.223, -2.078, -1.936, -1.798, -1.705, -1.616, -1.507, -1.405, -1.257, -1.091, -0.916, -0.713, -0.542, -0.386, -0.245, -0.121, -1.490E-2, 0.114, 0.254, 0.423, 0.612, 0.794, 0.959, 1.102, 1.229, 1.341, 1.437, 1.542, 1.671, 1.818, 1.976, 2.120, 2.271, 2.389, 2.476, 2.541, 2.598, 2.674, 2.761, 2.859, 2.967, 3.061, 3.146, 3.207, 3.233, 3.240, 3.246, 3.254, 3.261, 3.296]
+
+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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