'''
Compute the velocity curve of a force-time signal in Python
'''
import numpy as np
import matplotlib.pyplot as plt

# Define the force-time signal
t = np.linspace(0, 10, 1000)  # Time vector
f = np.sin(t) + np.random.normal(scale=0.1, size=t.shape)  # Simulated force signal with added noise

# Compute the velocity curve by numerical integration of the force signal
v = np.cumsum(f)  # Cumulative sum of the force signal
v -= np.mean(v)  # Remove any DC offset
dt = t[1] - t[0]  # Time step
v /= dt  # Divide by time step to get velocity

# Plot the force and velocity signals
fig, ax = plt.subplots()
ax.plot(t, f, label='Force')
ax.plot(t, v, label='Velocity')
ax.legend()
ax.set_xlabel('Time')
ax.set_ylabel('Force / Velocity')
plt.show()