A spring force depends on displacement from equilibrium
The mistake
Using F = kx without defining x from the spring's relaxed length or equilibrium point.
Why it feels right
Writing F_s = −kx without defining x hides the reference position that gives the sign meaning.
How to catch it
You plug in a position coordinate rather than spring stretch/compression.
The first principle
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.
A vertical spring stretches x₀ under a hanging mass. If pulled down an additional y, what is the extra restoring force?
Common wrong move
ky plus mg in the oscillation equation.
Correct
About equilibrium, the restoring force is -ky; gravity is already included in the shifted equilibrium.
Make a fresh prediction before referring to the worked example.