The sampling rate for all of the experiments was 50 Hz (50 samples per second, or dt= 0.02 seconds). In both files, the first column includes the acceleration data of the base support of the system, and the second column is the acceleration data of the degree of freedom (i.e., of the vibrating mass). All accelerations are in g. Using the acceleration data of the degree of freedom (i.e., of the vibrating mass), perform the following: A. Plot the the acceleration data of the degree of freedom versus the time (see example plots below). B. Find the peaks of the acceleration that occur during the free vibration (see example plots below). Tip: the signal processing toolbox has a function called findpeaks that can help you find the peaks. C. Estimate the period and the damping of the system from the first set of data (FreeVibrationSDOF_Data.txt) using three values of j cycles: (I) j = 10 cycles (II) j = 20 cycles (III) j = 30 cycles For each case C.I, C.II, and C.III using different starting peak (i.e., moving window of peaks). For example, peak,1 and peak,1+j 1 and Tn,1, peak,2 and peak,2+j 2 and Tn,2, ... Plot the variation of the damping ratio and the period of vibration with respect to the set of peak values you consider (see example plots at the end). Calculate the median value of damping ratio and natural period using the above estimates. [6] (4) 0.5 0.4 0.3 0.2 Acceleration Free vibration without added mass -0.1 -0.2 -0.3 -0.4 -0.5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 t [seconds] [6] (47) 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 [6] (4) 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 (t) [g] 0 5 10 15 20 Acceleration t [seconds] Acceleration Free vibration with added mass 25 30 35 40 45 Free vibration without added mass Peaks of interest -0.4 -0.5 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 t [seconds] 0.2 0.15 0.1 0.05 0 -0.05 -0.1 Acceleration Free vibration with added mass Peaks of interest -0.2 10 15 20 25 30 35 40 t [seconds] -0.15 "ACCEL_1" "ACCEL_2" "g" "g" 0.000228643 -0.000141382 -2.24E-05 -0.000176132 -3.03E-05 -0.000189632 -0.000191972 -0.000147223 -0.000102326 -3.84E-96 -0.000711933 0.000115335 0.000244468 0.000229657 8.09E-05 0.000203371 -6.37E-05 0.000189155 -0.000134811 0.000341415 2.16E-05 0.000387043 0.000477508 0.000426173 -0.000154182 0.000524461 -0.000172749 0.000549793 -0.000231475 0.000554591