A spring force depends on displacement from equilibrium
- 01
The tempting model
Using F = kx without defining x from the spring's relaxed length or equilibrium point.
- 02
Why it feels right
Writing F_s = −kx without defining x hides the reference position that gives the sign meaning.
- 03
Where it breaks · how to catch it
You plug in a position coordinate rather than spring stretch/compression.
- 04
The correct model
Hooke's law is F_s = −kΔx, where Δx is measured from the spring's relaxed length. In vertical SHM, use displacement from the shifted equilibrium for the oscillation.
- 05
Repair · see it, then test it
worked example A vertical spring stretches x₀ under a hanging mass. If pulled down an additional y, what is the extra restoring force?
Tempting move
ky plus mg in the oscillation equation.
Correct move
About equilibrium, the restoring force is -ky; gravity is already included in the shifted equilibrium.
Test the repair NL-15 · transferinclude NMake a fresh prediction before referring to the worked example.
Then practise it on the ladder
R18Spring turning pointadds: Spring energy is quadratic in displacement.