The oscillation of a single pendulum is 2.05s. What is the period of another simple pendulum which makes 300 vibration in the time it takes the first pendulum to make 200 vibrations?
the frequency is inversely proportional to the period
2.05 * 200 = p * 300
you're right
To find the period of the second pendulum, we can use the concept of proportional relationships.
Let's assume that the period of the second pendulum is represented by T2. We already know that the period of the first pendulum is 2.05 seconds, which we can represent as T1 = 2.05s.
We are given that the first pendulum makes 200 vibrations in the time it takes the second pendulum to make 300 vibrations. This implies that the time it takes for the first pendulum to make 200 vibrations is equal to the time it takes for the second pendulum to make 300 vibrations.
Using this information, we can set up the following proportion:
T1 / 200 = T2 / 300
Now, let's plug in the values we know:
2.05s / 200 = T2 / 300
To solve for T2, we can cross multiply and then divide:
2.05s * 300 = T2 * 200
615s = 200T2
T2 = 615s / 200
T2 ≈ 3.075s
Therefore, the period of the second simple pendulum is approximately 3.075 seconds.
To find the period of the second pendulum, we can use the concept of ratio and proportion.
First, let's determine the period of the first pendulum. The oscillation time of the first pendulum is given as 2.05 seconds, and it makes 200 vibrations in that time. Therefore, the period of the first pendulum is:
Period of first pendulum = 2.05 seconds / 200 vibrations = 0.01025 seconds/vibration
Now, let's calculate the period of the second pendulum using the information provided. The second pendulum makes 300 vibrations in the time it takes the first pendulum to make 200 vibrations.
By setting up a proportion, we can find the period of the second pendulum:
Period of first pendulum / Period of second pendulum = Number of vibrations for first pendulum / Number of vibrations for second pendulum
0.01025 seconds/vibration / Period of second pendulum = 200 vibrations / 300 vibrations
Cross-multiplying, we get:
0.01025 seconds/vibration = (200 / 300) * Period of second pendulum
0.01025 seconds/vibration = 0.6667 * Period of second pendulum
Now, isolate the Period of the second pendulum:
Period of second pendulum = 0.01025 seconds/vibration / 0.6667
Period of second pendulum ≈ 0.015376 seconds/vibration
Therefore, the period of the second pendulum is approximately 0.015376 seconds/vibration.