calculate_simple_harmonic_motion
Calculate position, velocity, and acceleration for oscillating systems like springs and pendulums using the simple harmonic motion equation x(t) = A cos(ωt + φ).
Instructions
Calculate simple harmonic motion: x(t) = A cos(ωt + φ).
Position, velocity, and acceleration for sinusoidal oscillation.
Models ideal springs, pendulums, and many other oscillating systems.
Args:
amplitude: Amplitude A in meters (maximum displacement)
angular_frequency: ω in rad/s (ω = 2πf)
time: Time t in seconds
phase: Phase shift φ in radians (default 0)
Returns:
Dict containing:
- position: x(t) in meters
- velocity: v(t) = -Aω sin(ωt + φ) in m/s
- acceleration: a(t) = -Aω² cos(ωt + φ) in m/s²
Tips for LLMs:
- Position and acceleration are 180° out of phase
- Maximum velocity occurs at equilibrium (x = 0)
- Maximum acceleration occurs at maximum displacement
Example - Oscillating mass:
result = await calculate_simple_harmonic_motion(
amplitude=0.1, # 10cm amplitude
angular_frequency=5.0, # rad/s
time=1.0 # at t = 1s
)Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| amplitude | Yes | ||
| angular_frequency | Yes | ||
| time | Yes | ||
| phase | No |