Final answer:
The periods of two pendulums with the same lengths are equal, irrespective of the bobs' masses. Mass does not influence the frequency of a simple pendulum; it depends solely on the string's length and gravity's acceleration.
Step-by-step explanation:
When comparing two pendulums with the same length but different masses, the periods of the pendula remain unchanged. The period of a simple pendulum is independent of the mass of the bob and is only influenced by the length of the string and the acceleration due to gravity. Thus, even though Pendulum 1 has a mass of 0.1 kg and Pendulum 2 has a mass of 0.5 kg, the mass does not affect their frequencies.
The period T of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula shows that the period (and thus the frequency, which is the reciprocal of the period) is dependent on the length of the pendulum, not its mass. Consequently, two pendulums with the same length will have the same period, regardless of their respective masses.
However, it is important to note that the question also references two pendulums with different lengths. In that case, the frequency of the pendulum will be higher for the pendulum with the shorter length due to the inverse relationship between the period and the square root of the length.