calculate_damped_oscillation
Calculate position and velocity of damped oscillators with friction or resistance. Determine damping regimes (underdamped, critically damped, overdamped) for systems like car suspensions or mechanical oscillators.
Instructions
Calculate damped oscillation with friction/resistance.
Real oscillators lose energy over time due to damping (air resistance,
friction). Three regimes: underdamped, critically damped, overdamped.
Args:
mass: Mass in kg
spring_constant: k in N/m
damping_coefficient: b in kg/s (damping strength)
time: Time t in seconds
initial_position: Initial position in meters (default 1.0)
initial_velocity: Initial velocity in m/s (default 0.0)
Returns:
Dict containing:
- position: x(t) in meters
- velocity: v(t) in m/s
- damping_ratio: ζ (zeta) = b/(2√(mk))
- regime: "underdamped", "critically_damped", or "overdamped"
Damping regimes:
- ζ < 1: Underdamped (oscillates, gradually decays)
- ζ = 1: Critically damped (returns fastest without oscillating)
- ζ > 1: Overdamped (slow return, no oscillation)
Example - Car suspension:
result = await calculate_damped_oscillation(
mass=300, # kg (quarter car mass)
spring_constant=20000, # N/m
damping_coefficient=2000, # kg/s
time=1.0
)
# Should be slightly underdamped for comfortInput Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| mass | Yes | ||
| spring_constant | Yes | ||
| damping_coefficient | Yes | ||
| time | Yes | ||
| initial_position | No | ||
| initial_velocity | No |