Separate the three points
The centre falls while the bottom stays put
01 / topGravity and spring contraction pull in the same direction. The upper coils pack together behind the front.
02 / centreFalls with gravitational acceleration. Without air resistance, displacement is ½ × 9.81 × t².
03 / bottomRemains almost motionless. Local tension keeps balancing its weight until the front arrives.
35.8 cmideal fall of the centre of mass in 0.27 seconds
What happens at the bottom
The forces were already balanced
Before release, every part of the spring is stationary. For the lower coils, downward weight is matched by upward tension. Releasing the top changes the tension there first.
The front travels through the spring as coils behind it collide and pack together. Once it reaches the bottom, the tension supporting the last coils collapses; their downward movement starts at that point.
Two very different springs
The same collapse time in both fits
Cross and Wheatland filmed a metal and a plastic Slinky at 300 frames per second. Their masses differ by 4.43× and their fitted spring constants by 3.14×. Both model fits gave 0.27 seconds for complete collapse.
| Quantity | Metal | Plastic |
|---|---|---|
| Mass | 215.5 grams | 48.7 grams |
| Stretched length | 1.26 metres | 1.14 metres |
| Turns | 86 turns | 39 turns |
| Fitted constant | 0.69 N/m | 0.22 N/m |
| Collapse time | 0.27 seconds | 0.27 seconds |
Method and limits
The camera measures; the model explains
The camera recorded 300 frames per second, or about 3.33 milliseconds between frames. The authors tracked positions every 10 milliseconds and fitted a model in which tension decays gradually behind the front. In the illustrated sequence, turns 8 and 10 changed from stretched to compressed over about 0.1 seconds.
The model reproduces the top trajectory qualitatively. Calculated fundamental periods differ from observed periods by 2.3% for the metal spring and 6.2% for the plastic one, below the representative 8% estimate discussed by the authors. Suspension, air resistance, coil contact and specimen differences keep 0.27 seconds tied to these two drops.
A 2025 analysis explicitly included the tied top turns in its model, a feature absent from the earlier model discussed here. The authors derive explicit trajectories for the top's position, velocity and acceleration, with good agreement with measurements. The suspension effect has therefore been modelled in later work, while the 0.27-second value remains tied to the two filmed specimens and the assumptions used.
Unruh's analysis separates the mathematical case in which coils pass through one another from the physical case in which they collide. The real spring forms a shock front, while mechanical energy lost in collisions becomes heat and vibration.