API Reference

Linear Motion

linear_motion.calculate_linear_motion(initial_position: float, initial_velocity: float, acceleration: float, time: float = 0.0) → Dict[str, float]

Calculates the kinematic values for linear motion

Parameters:

• initial_position – The initial position of the particle in m

• initial_velocity – The initial velocity of the particle in m/s

• acceleration – The constant acceleration in m/s^2

• time – The time in the final position in s

Returns:

A dictionary containing the final position and the final velocity

Projectile Motion

projectile.calculate_kinematics(initial_velocity: float, launch_angle: float) → Dict[str, float]

Calculates the kinematic parameters for projectile motion

Parameters:

• initial_velocity – The initial velocity of the projectile in m/s

• launch_angle – The launch angle in degrees

Returns:

A dictionary containing the time of flight, max height, and horizontal range

Damped Harmonic Oscillator

oscillations.calculate_oscillation(mass: float, spring_constant: float, damping_coefficient: float = 0.0) → Dict[str, float]

Calculates the characteristic properties of a damped harmonic oscillator

Parameters:

• mass – Mass on the spring in kg

• constant (spring) – Spring constant k in N/m

• coefficient (damping) – Damping coefficient b in kg/S (0=undamped)

Returns:

A dictionary with natural angular frequency, natural frequency, period, damping ratio and the oscillation regime

oscillations.displacement(t: ndarray, mass: float, spring_constant: float, amplitude: float, damping_coefficient: float = 0.0) → ndarray

Position x(t) for a damped harmonic oscillator released from rest at x = amplitude (initial conditions x(0)=A, v(0)=0)