For spring-mass systems: the time period is unaffected by acceleration of the frame because the spring force depends only on extension, not gravity. For pendulums: use effective gravity $\vec{g}_{\text{eff}} = \vec{g} - \vec{a}_{\text{frame}}$. Elevator going up: $g_{\text{eff}} = g + a$, $T$ decreases. Going down: $g_{\text{eff}} = g - a$, $T$ increases. Horizontal acceleration: $g_{\text{eff}} = \sqrt{g^2 + a^2}$, equilibrium angle shifts to $\theta = \tan^{-1}(a/g)$ from vertical.