Spring Physics

See how a spring naturally produces a sine wave (press play):

(Note: you can drag the end of the spring.)

Why Does It Make a Sine Wave?

When you pull the spring down and let go, two main things happen:

• The Restoring Force: The further you pull the spring, the harder it pulls back. This is called Hooke's Law:
  
  F = −kx
  (Where F is the force, x is how far you stretched or compressed it, and k is the stiffness of the spring).
• Momentum: As the spring pulls the weight back to the middle (the equilibrium point), the weight speeds up. When it reaches the middle, the restoring force drops to zero, but the weight is moving so fast that its momentum carries it right past, compressing the spring!

This continuous trade-off between potential energy (stored in the spring) and kinetic energy (movement) creates a smooth oscillation called Simple Harmonic Motion.