To find the period of the second pendulum, we can set up a proportion based on the number of vibrations made by each pendulum.
Let's assume the period of the second pendulum is T2 (in seconds).
According to the given information: The period of the first pendulum is 2.05 seconds, and it makes 200 vibrations. The period of the second pendulum is T2 seconds, and it makes 300 vibrations.
We can set up the proportion:
(T1 / N1) = (T2 / N2),
where T1 is the period of the first pendulum, N1 is the number of vibrations made by the first pendulum, T2 is the period of the second pendulum, and N2 is the number of vibrations made by the second pendulum.
Plugging in the values we know:
(2.05 s / 200) = (T2 / 300).
We can now solve for T2 by cross-multiplying and rearranging the equation:
2.05 s * 300 = T2 * 200,
615 s = T2 * 200.
Dividing both sides of the equation by 200:
615 s / 200 = T2,
3.075 s = T2.
Therefore, the period of the second pendulum is approximately 3.075 seconds when it makes 300 vibrations, which is the same time it takes for the first pendulum to make 200 vibrations.