For a spring-mass system on a frictionless surface, $T = 2\pi\sqrt{m/k}$. Key features: (1) Independent of amplitude — a hallmark of SHM. (2) Independent of gravity — a horizontal spring oscillates identically on Earth, Moon, or in space. (3) For a vertical spring, the equilibrium position shifts by $mg/k$ but the time period remains $2\pi\sqrt{m/k}$. Students often wrongly think gravity affects the time period of a spring system.