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Tune the Period

Tune a block on a spring to keep time with a metronome. Change the mass or the springs.

Physics · Class 11 · Spring and mass · 10 simulations. For JEE, NEET and your boards.

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What you'll learn

  1. Keep the beat: T = 2π√(m/k)
  2. Add a lump: Same spring: T² grows with m
  3. Two in a line: In a line: 1/k = 1/k₁ + 1/k₂
  4. Held from both sides: Both sides push back: k = k₁ + k₂
  5. Line or side by side: Same block, new springs: T ∝ 1/√k
  6. Stiff one way: Two half swings: T = π√(m/k₁) + π√(m/k₂)
  7. Switch on a push: A steady push moves the centre, not the beat
  8. Two carts: Two free bodies: use μ = m₁m₂/(m₁ + m₂)
  9. Who moves more: The centre of mass stays still: m₁A₁ = m₂A₂
  10. Putty in a cart: Hit first, then the spring takes ½μv²