Final answer:
The period of a pendulum is directly proportional to the square root of its length. If one pendulum has length L and another has length 4L, the second pendulum's period is twice that of the first.
Step-by-step explanation:
The period of a pendulum, denoting the time for one complete swing, is intricately tied to its length. Mathematically expressed as T = √L, where T is the period and L is the length, this equation reveals a direct proportionality between these variables.
Consider two pendulums: one with length L and the other with 4L.
Applying the formula, T2 = √(4L), simplifies to T2 = 2√L.
Consequently, the period of the second pendulum is twice that of the first when the second pendulum's length is four times greater. This square root relationship underscores the nuanced influence of length on the period, illustrating a proportional increase in the time required for a complete oscillation as the pendulum's length expands. The intricacies of this connection highlight the elegant simplicity underlying the physics of pendulum motion.