plt.style.use('dark_background')
theta = np.linspace(0, 180, 500)
equilibrium = np.poly1d([11.946862470797765, 29.288529089840527, 1.0401199115394326])
plt.plot(theta, equilibrium(np.sin(np.radians(theta))))
plt.grid(True)
plt.xticks([0, 30, 60, 90, 120, 150, 180])
plt.title("Required input for force equilibrium as function of pendulum angle")
plt.xlabel(r"Pendulum Angle ($\degree$)")
plt.ylabel("Equilibrium Input (%)")