import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import TransferFunction, step

def step_response(T, t_end):
    # Define the transfer function H(s) = (-Ts + 1) / (s^3 + 3s^2 + 2s + 1)
    num = [-T, 1]
    den = [1, 3, 2, 1]
    system = TransferFunction(num, den)

    # Generate time points
    t = np.linspace(0, t_end, 1000)
    
    # Calculate the step response
    t, response = step(system, T=t)
    
    # Plot the step response
    plt.plot(t, response)
    plt.title('Step Response of the System')
    plt.xlabel('Time (s)')
    plt.ylabel('Response')
    plt.grid(True)
    plt.show()
    
    return t, response

# Example usage
T = 1  # Time constant
t_end = 10  # seconds

t, response = step_response(T, t_end)