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Position, Velocity, and Acceleration in SHM

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About This MicroSim

This simulation shows a mass-spring system undergoing simple harmonic motion with synchronized real-time graphs of position, velocity, and acceleration.

Key Relationships

  • Position: x(t) = A cos(ωt)
  • Velocity: v(t) = -Aω sin(ωt)
  • Acceleration: a(t) = -Aω² cos(ωt) = -ω²x

Phase Relationships

  • Position and acceleration are 180° out of phase (opposite signs)
  • Velocity leads position by 90° (quarter cycle)
  • When x is maximum, v = 0 and a is maximum negative
  • When x = 0, v is maximum and a = 0

Controls

  • Amplitude slider: Change maximum displacement
  • Frequency slider: Change oscillation speed
  • Show vectors: Display velocity and acceleration arrows on mass
  • Pause/Reset: Control the animation

Lesson Plan

Discussion Questions

  1. Why is velocity zero at maximum displacement?
  2. Why is acceleration maximum at maximum displacement?
  3. What is the relationship between a and x?