Visual walkthrough — Damped oscillations — underdamped, critically damped, overdamped

We assume only that you know a spring pulls back and that "faster means more air-drag." Everything else — every symbol — is built here.

---

Step 1 — Draw the two forces on the mass

WHAT. Two arrows act on the block.

• The spring force $-kx$: if you pull right ($x>0$) it pulls left, so it carries a minus sign. Bigger stretch → bigger pull.
• The drag force $-b\dot{x}$: it always points opposite the velocity. The number $b>0$ is the damping constant — how thick the "syrup" is.

**WHY these two and noth