Final answer:
The period of a pendulum is unaffected by changes in the mass of the pendulum bob; it is determined by the length of the pendulum and gravity. Consequently, if two pendula have the same length and are under the same gravitational force, they will have the same period regardless of their differing masses.
Step-by-step explanation:
When the mass of a pendulum bob is increased, the period of the pendulum is not affected. This is because the period of a simple pendulum is determined by its length and the acceleration due to gravity, not the mass of the bob. A pendulum with a mass of 10 kg and a pendulum with a mass of 100 kg will have the same period if they have the same length and are subject to the same gravitational acceleration. Therefore, when displaced by 12°, the motion of the pendula will be identical regardless of the difference in mass.