Final answer:
Both pendulums, despite having different bob masses, will swing with the same period when displaced by 12º because the period of a simple pendulum is independent of the mass of the bob.
Step-by-step explanation:
The question pertains to the dynamics of simple pendula and their motion under gravitational influence. Both pendulums, despite having different bob masses, will swing with the same period when displaced by 12º because the period of a simple pendulum is independent of the mass of the bob.
Specifically, it examines how the mass of a pendulum bob affects its swing when displaced by the same angle. Despite the different masses (10 kg and 100 kg), both pendulums will have the same period because the period of a simple pendulum in small-angle approximation is independent of mass and primarily depends on the length of the tether and the gravitational acceleration.
Thus, when both bobs are displaced by 12º, they will swing with the same frequency, assuming that air resistance, the mass of the string, and other non-ideal factors do not significantly affect the motion.