Final answer:
To find the new period of the pendulum with a different mass and a longer string, we use the formula for the period of a simple pendulum, which only depends on the length of the string and the acceleration due to gravity. The new period is found by replacing the original length L with 5.20L in the period formula.
Step-by-step explanation:
The question concerns the period of oscillation of a pendulum, which is determined by the mass of the bob and the length of the string. Initially, a bob with mass m suspended from a string of length L has a period of 2.0 s. When the bob is replaced by one with mass 1/3m and the string length is increased to 5.20L, we can use the formula for the period of a simple pendulum, T = 2π√(L/g), where g is the acceleration due to gravity. Since the period is independent of the mass of the bob, we can ignore the change in bob mass and focus purely on the change in the string length. After replacing L in the formula with 5.20L, the new period can be calculated.