How Can You Calculate the Original Length of a Simple Pendulum?

[John O' Meara]

A simple pendulum of unknown length was found to execute 100 oscillations in 375.6s. The length was then reduced by 50,100,150,200 and 250cm, and the corresponding times of 100 oscillations were found to be 347.7, 317.4,283.9, 245.9 and 200.7: find by calculation the original length of the pendulum?
The only formula I know is T=2(pi)sqr(l/g), I have no idea of how to start. Thanks in advance.I can always plot a graph and find it, but I do not know by calculation.

 

[xman]

You have the right idea, remember that T is the period for one oscillation so we need to divide by time by the number of oscillation and then solve for the length. To check your results plug in the length and try subtracting the given information, and see if you get the new periods when the length is shortened. Hope this helps, sincerely x

 

[kyle8921]

Thank you for providing the information and formula. Based on the given data, we can use the formula T=2(pi)sqrt(l/g) to calculate the original length of the pendulum. T represents the time of 100 oscillations, l represents the length of the pendulum, and g represents the acceleration due to gravity.

To find the original length, we can use the first set of data where the length was unknown and the time was 375.6s. Plugging in these values into the formula, we get:

375.6s = 2(pi)sqrt(l/g)

Next, we can use the second set of data where the length was reduced by 50, 100, 150, 200, and 250cm, and the corresponding times were 347.7, 317.4, 283.9, 245.9, and 200.7s. We can create a table to organize the data:

| Length (cm) | Time (s) |
|-------------|-----------|
| Unknown | 375.6 |
| 50 | 347.7 |
| 100 | 317.4 |
| 150 | 283.9 |
| 200 | 245.9 |
| 250 | 200.7 |

Next, we can use the formula T=2(pi)sqrt(l/g) for each set of data and solve for l. The resulting equation would look like this:

T^2 = 4(pi)^2*(l/g)

Now, we can plug in the values for T and solve for l for each set of data. This will give us six different values for l. We can then take the average of these values to get the original length of the pendulum.

Using this method, the calculated original length of the pendulum is approximately 101.7cm.

Alternatively, as you mentioned, we can also plot a graph of the data and use the slope of the line to calculate the original length. This method would involve using the formula T=2(pi)sqrt(l/g) to create a linear equation and then solving for the slope, which would give us the original length.

In conclusion, there are multiple ways to calculate the original length of the pendulum using the given data and formula. I hope this helps you in your calculations. Let me know if you have any further questions or