calculate_pendulum_period
Calculate the period of a simple pendulum given its length and gravitational acceleration. Supports large-angle corrections for accurate results.
Instructions
Calculate pendulum period: T = 2π√(L/g).
Period of a simple pendulum depends only on length and gravity
(for small amplitudes). Includes correction for large amplitudes.
Args:
length: Pendulum length in meters (pivot to center of mass)
gravity: Gravitational acceleration in m/s² (default 9.81)
amplitude_degrees: Amplitude in degrees (optional, for large angle correction)
Returns:
Dict containing:
- period: T in seconds
- frequency: f in Hz
- angular_frequency: ω in rad/s
- small_angle_approximation: Whether small angle formula was used
Tips for LLMs:
- Period independent of mass (Galileo's discovery)
- Period independent of amplitude (for small angles < 15°)
- Longer pendulum → longer period
- Use for: clocks, playground swings, seismometers
Example - Grandfather clock:
result = await calculate_pendulum_period(
length=0.994, # meters (for 2-second period)
gravity=9.81
)
# T = 2.0 secondsInput Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| length | Yes | ||
| gravity | No | ||
| amplitude_degrees | No |