A pendulum 0.80 m long hangs in a lift. Find its period (a) when the lift is at rest, (b) when the…

(a) At rest. $T = 2\pi\sqrt{\dfrac{0.80\ \text{m}}{9.8\ \text{m/s}^2}} = 1.80\ \text{s}$.

(b) Speeding up upwards. $g_{\text{eff}} = 9.8\ \text{m/s}^2 + 2.6\ \text{m/s}^2 = 12.4\ \text{m/s}^2$, so $T = 2\pi\sqrt{\dfrac{0.80\ \text{m}}{12.4\ \text{m/s}^2}} = 1.60\ \text{s}$.

(c) Speeding up downwards. $g_{\text{eff}} = 9.8\ \text{m/s}^2 - 2.6\ \text{m/s}^2 = 7.2\ \text{m/s}^2$, so $T = 2\pi\sqrt{\dfrac{0.80\ \text{m}}{7.2\ \text{m/s}^2}} = 2.09\ \text{s}$.

(d) Free fall. $g_{\text{eff}} = 0$. Nothing pulls the bob back, so the pendulum does not swing. It stays wherever it is, relative to the lift.