SHM needs a linear restoring force

The mistake

Calling any back-and-forth motion simple harmonic.

Why it feels right

Lots of oscillations look sinusoidal at a glance.

How to catch it

You applied ω = √(k/m) to a system whose restoring force isn't ∝ −x.

The first principle

SHM requires F = −kx (restoring force proportional to displacement). A pendulum is SHM only in the small-angle limit where sin θ ≈ θ.

worked mini-example

Is a ball bouncing on the floor simple harmonic?

Common wrong move

Yes — it repeats.

Correct

No — the force isn't −kx; the motion isn't sinusoidal.

Test the repair SHM-01 · transfer

A particle feels F = −bx³. Is its full motion simple harmonic?

Yes, because the force points toward equilibrium Yes, because the force is odd in x No, because the restoring force is not proportional to x No, because acceleration must be zero

Make a fresh prediction before referring to the worked example.