Consider the clock shown in Figure DP2.5. The pendulum rod of length L supports a pendulum disk.

Assume that the pendulum rod is a massless rigid thin rod and the pendulum disc has mass m. Design the length of the pendulum, L, so that the period of motion is 2 seconds. Note that with a period of 2 seconds each “tick” and each “tock” of the clock represents 1 second, as desired. Assume small angles, ϕ(t), in the analysis so that sin ϕ(t) L ϕ(t). Can you explain why most grandfather clocks are about 1.5 m or taller?

"tick" "tock" 1 second later... FIGURE DP2.5 (a) Typical clock (photo courtesy of Science and Society/ SuperStock) and (b) schematic representation of the pendulum. Pendulum rod Pendulum disk (a) (1) m m g (b) g -p(t)