LUDO › Simulations › Simple Harmonic Motion

Phase Match

Turn a circle and watch its shadow swing. Set the phase so it moves in step.

Physics · Class 11 · SHM as the shadow of a circle · 9 simulations. For JEE, NEET and your boards.

A picture of the Phase Match simulation

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What you'll learn

  1. Shadow of a circle: A steady turn casts an SHM shadow: ω = √(k/m)
  2. Speed at a point: Speed from the circle: v = ω√(A² − x²)
  3. Read the ellipse: The v–x law: v² = ω²(A² − x²)
  4. Start in step: The start angle: cos θ₀ = x₀/A, and the way it moves
  5. Sine start: The sine form: x = A sin(ωt + φ)
  6. The slow half: Time on the circle: t = (angle turned / 360°) × T
  7. Two and a quarter swings: Distance in SHM: 4A for each whole swing
  8. Arrows at right angles: Add SHMs like arrows: R² = A₁² + A₂² + 2A₁A₂ cos δ
  9. Equal arrows: The gap from the sum: cos δ = (R² − A₁² − A₂²)/(2A₁A₂)