Two simple pendula x and y make 400 and 500 oscillations respectively in equal time. If the period of oscillation of x is 1.5 seconds, what is the period of...

Two simple pendula x and y make 400 and 500 oscillations respectively in equal time. If the period of oscillation of x is 1.5 seconds, what is the period of oscillation of y?

Answer Details

The number of oscillations of a pendulum in a given time depends on its period of oscillation. The period is the time taken for one complete oscillation. The relationship between the period and the number of oscillations is direct; that is, as the period of a pendulum decreases, the number of oscillations it makes in a given time increases. In this question, we are given that the period of oscillation of pendulum x is 1.5 seconds, and it makes 400 oscillations in equal time. We are also given that pendulum y makes 500 oscillations in equal time. Since both pendula are making oscillations in equal time, we can assume that the time taken for each pendulum to make one oscillation is the same. To find the period of oscillation of pendulum y, we can use the relationship between the period and the number of oscillations. If pendulum x with a period of 1.5 seconds makes 400 oscillations in equal time, then the total time taken for 400 oscillations is: Time taken by pendulum x = 400 x 1.5 seconds = 600 seconds Since pendulum y makes 500 oscillations in the same time, the period of oscillation of y can be calculated as follows: Time taken by pendulum y for 500 oscillations = 600 seconds Period of pendulum y = Total time taken / Number of oscillations Period of pendulum y = 600 seconds / 500 oscillations Period of pendulum y = 1.2 seconds Therefore, the period of oscillation of pendulum y is 1.2 seconds.