Lab Report 2_ Pendulum I - Frank Dong, Ayesha Minal, and Samantha Lattuca

15 22.65 Figure 3: Raw data reporting time and peak number in excel table E1 - Data Analysis From the excel data from Figure 3 the difference in time between each consecutive peak was calculated, giving us 14 measurements. The differences were calculated using the subtraction function on excel and not by hand. Moreover, an average period along with its uncertainty (standard deviation) were also found using excel functions. Peak Number Time (s) Differences (s) 1 1.12 2 2.65 1.53 3 4.26 1.61 4 5.71 1.45 5 7.32 1.61 6 8.85 1.53 7 10.38 1.53 8 11.91 1.53 9 13.46 1.55 10 14.99 1.53 11 16.52 1.53 12 18.05 1.53 13 19.58 1.53 14 21.11 1.53 15 22.65 St. Dev. Avg Period 1.53769231s 0.039613518s Avg Freq 0.65032516Hz Figure 4: Table showing differences in time between peaks

3 4.51 4 5.99 5 7.59 6 9.07 7 10.53 8 12.14 9 13.6 10 15.08 11 16.68 12 18.15 13 19.62 14 21.09 15 22.69 Figure 8: Raw data with peak number and time from Experiment 2 E2 - Data Analysis From the raw data table, a difference function from excel was used to determine the difference in time between peaks. Furthermore, the average and standard deviation (uncertainty) was calculated: Peak Number Time (s) Differences (s) 1 1.45 2 3.05 1.6 3 4.51 1.46 4 5.99 1.48 5 7.59 1.6 6 9.07 1.48 7 10.53 1.46 8 12.14 1.61 9 13.6 1.46

period (FFT) was 1.4925 s. The difference between the first period and third period is 0.045 s and the difference between the second period and third period is 0.02 s. Overall, all three methods led this experiment to being successful. Exercise 3: Calculate the Length of Your Pendulum E3 - Data Collection In this exercise, we used the period we obtained from exercise 2.2, which was 1.514 s to calculate the theoretical length of the pendulum. The formula T = 2π(L/g) ½ was rearranged to solve for T (as was done in the prelab). The theoretically determined and actual lengths of the pendulum were then reported and compared. Figure 12: Measuring the length of the pendulum E3 - Data Analysis L = (gT 2 )/(4π 2 ) = ((9.81 m/s 2 )*(1.514 s) 2 )/(4π 2 ) L = 0.5696 m Value of L using measuring tape: 57.912 cm = 0.58 m E3 - Conclusion The value of L was calculated to be 0.5699 m, and 0.58 m when it was physically measured with a measuring tape. These values are very close to one another, helping validate the experiment. Final Conclusion Overall, we were very successful in this lab as the values that we found experimentally and through calculations were very similar. We concluded that the equation we previously derived for the length (L) was accurate.The methods we used to calculate the period in both exercises were accurate as we ended up with similar results. In non-perfect conditions like this lab, some