Calculation of the Time Period:

To find the percentage error in the measured value of the time period, we first need to calculate the average time period of the simple pendulum. The average is calculated by summing up the individual time periods and dividing by the number of observations.

Given time periods:
T1 = 3.60s
T2 = 3.72s
T3 = 3.68s

Average time period (T_avg) = (T1 + T2 + T3) / 3

Substituting the values:
T_avg = (3.60 + 3.72 + 3.68) / 3 = 3.67s

Percentage Error Calculation:

The percentage error is calculated by finding the difference between the measured value and the accepted value, dividing it by the accepted value, and then multiplying by 100.

Percentage Error = ((Measured Value - Accepted Value) / Accepted Value) * 100

In this case, the accepted value can be considered as the average time period obtained from the measurements, which is 3.67s.

Let's calculate the percentage error for each individual measurement:

Percentage Error (T1) = ((3.60 - 3.67) / 3.67) * 100
Percentage Error (T2) = ((3.72 - 3.67) / 3.67) * 100
Percentage Error (T3) = ((3.68 - 3.67) / 3.67) * 100

Calculating the values:
Percentage Error (T1) = (-0.07 / 3.67) * 100 = -1.91%
Percentage Error (T2) = (0.05 / 3.67) * 100 = 1.36%
Percentage Error (T3) = (0.01 / 3.67) * 100 = 0.27%

Average Percentage Error Calculation:

To find the average percentage error, we sum up the individual percentage errors and divide by the number of observations.

Average Percentage Error = (|Percentage Error (T1)| + |Percentage Error (T2)| + |Percentage Error (T3)|) / 3

Calculating the values:
Average Percentage Error = (1.91 + 1.36 + 0.27) / 3 = 1.18%

Explanation:

The percentage error is a measure of the accuracy of the measured value compared to the accepted value. It indicates the deviation of the measured value from the true value and expresses it as a percentage.

In this case, we calculated the average time period of the simple pendulum using the given observations. Then we calculated the percentage error for each individual measurement by comparing it with the average time period. Finally, we found the average percentage error by taking the absolute values of the individual percentage errors and averaging them.

The negative percentage error for T1 indicates that the measured value is lower than the accepted value, while the positive percentage errors for T2 and T3 indicate that the measured values are higher than the accepted value. The average percentage error of 1.18% suggests that the measured values, on average, deviate from the true value by approximately 1.18%.

It is important to note that reducing the percentage error requires improving the accuracy of the