answer:import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation from scipy.integrate import odeint from ipywidgets import interact, widgets from IPython.display import display class DoublePendulum: def __init__(self, length1=1.0, length2=1.0, mass1=1.0, mass2=1.0): self.length1 = length1 self.length2 = length2 self.mass1 = mass1 self.mass2 = mass2 def equations(self, y, t): theta1, z1, theta2, z2 = y c, s = np.cos(theta1 - theta2), np.sin(theta1 - theta2) theta1dot = z1 theta2dot = z2 z1dot = (self.mass2 * self.length2 * z2**2 * s * c + self.mass2 * 9.81 * np.sin(theta2) * c + self.mass2 * self.length2 * z2**2 * s - (self.mass1 + self.mass2) * 9.81 * np.sin(theta1)) / (self.length1 * (self.mass1 + self.mass2 * s**2)) z2dot = ((self.mass1 + self.mass2) * (self.length1 * z1**2 * s - 9.81 * np.sin(theta2) + 9.81 * np.sin(theta1) * c) + self.mass2 * self.length2 * z2**2 * s * c) / (self.length2 * (self.mass1 + self.mass2 * s**2)) return theta1dot, z1dot, theta2dot, z2dot def animate_pendulum(length1, length2): pendulum = DoublePendulum(length1, length2) y0 = [np.pi / 2, 0, np.pi / 2, 0] t = np.linspace(0, 10, 250) solution = odeint(pendulum.equations, y0, t) x1 = pendulum.length1 * np.sin(solution[:, 0]) y1 = -pendulum.length1 * np.cos(solution[:, 0]) x2 = x1 + pendulum.length2 * np.sin(solution[:, 2]) y2 = y1 - pendulum.length2 * np.cos(solution[:, 2]) fig = plt.figure() ax = fig.add_subplot(111, autoscale_on=False, xlim=(-2, 2), ylim=(-2, 2)) ax.set_aspect('equal') ax.grid() line, = ax.plot([], [], 'o-', lw=2) time_template = 'time = %.1fs' time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes) def init(): line.set_data([], []) time_text.set_text('') return line, time_text def update(i): x = [0, x1[i], x2[i]] y = [0, y1[i], y2[i]] line.set_data(x, y) time_text.set_text(time_template % t[i]) return line, time_text ani = animation.FuncAnimation(fig, update, frames=np.arange(len(t)), init_func=init, blit=True) def save_animation(file_name): Writer = animation.writers['ffmpeg'] writer = Writer(fps=15, metadata=dict(artist='Me'), bitrate=1800) ani.save(file_name, writer=writer) plt.show() display(widgets.Text(value='animation.mp4', description='Filename:'), widgets.Button(description="Save as")) def on_button_clicked(b): file_name = widget_text.value save_animation(file_name) widget_text = widgets.Text(value='animation.mp4', description='Filename:') button = widgets.Button(description="Save as") button.on_click(on_button_clicked) display(widget_text, button) interact(animate_pendulum, length1=widgets.FloatSlider(min=0.1, max=2.0, step=0.1, value=1), length2=widgets.FloatSlider(min=0.1, max=2.0, step=0.1, value=1));

answer:def truncate_unique_chars(s): Truncates the input string to display only the first 4 unique characters in alphabetical order. If the string has less than four unique characters, display the unique characters only. # Create a set to capture unique characters and sort them alphabetically unique_chars = sorted(set(s)) # Get the first 4 unique characters truncated_chars = unique_chars[:4] # Join the list of characters into a string and return return ''.join(truncated_chars)

answer:def fibonacci(n): Generates the first n numbers of the Fibonacci series. fib_series = [0, 1] if n <= 0: return [] elif n == 1: return [0] else: while len(fib_series) < n: next_value = fib_series[-1] + fib_series[-2] fib_series.append(next_value) return fib_series[:n] def even_fibonacci(n): Generates the first n numbers of the Fibonacci series and returns only the even numbers. fib_series = fibonacci(n) return [num for num in fib_series if num % 2 == 0]

answer:def sort_and_reverse(arr): Sorts the array in ascending order and then reverses it. arr.sort() arr.reverse() return arr