Please complete the following:

The Pendulum Observations: Changing Amplitude (Procedure #2) Table 1 Time for 20 cycles Length Amplitude Average Frequency (cm) (cm) Time for H2 100 200 10 44.82 44.09 44.02 44.31 0.45 Hz seconds seconds seconds seconds 100 200 20 43.64 43.36 43.02 43.35 0.46 Hz seconds seconds seconds seconds 100 200 30 43.40 43.09 43.82 43.44 0.46 Hz seconds seconds seconds seconds Changing Mass (Procedure #3) Table 2 Time for 20 cycles Length Amplitude Trials: Average (cm) (cm) Time for 20 100 50 10 42.57 42.82 42.73 42.71 0.47 Hz seconds seconds seconds seconds 100 100 10 42.44 42.39 42.77 42.53 0.47 HZ seconds seconds seconds seconds 100 200 10 44.82 44.09 44.02 44.31 0.45 Hz seconds seconds seconds seconds Changing Length (Procedure #4) Table 3 Time for 20 cycles Length Amplitude Trials: ''"' '"" II 100 100 10 42.44 47 34 42.77 seconds seconds seconds 100 10 36.58 36.15 36.00 seconds seconds seconds 100 10 33.65 33.38 33.95 seconds seconds seconds 100 10 26.65 26.28 26.48 seconds seconds seconds 20 100 10 20.07 20.04 20.17 seconds seconds seconds Average Time for 20 cycles 42.53 seconds 36.24 seconds 33 .66 seconds 26.47 seconds 20. 1 1 seconds Analysis: Part I Determine Relationships 1. Plot the following graphs: a. Frequency versus Amplitude (Table 1); b. Frequency versus Mass (Table 2); and 0. Frequency versus Length (Table 3). 2. What is the relationship between: a. Amplitude and Frequency? b. Mass and Frequency? \fPart II - Determining Acceleration due to Gravity: THEORY To determine the acceleration due to gravity, we will use a common technique in physics in regards to graphical analysis. Our measured values from the experiment are the period T and the length of the pendulum I. Rewrite Eqn(1) as T=2\" g f And compare to the linear expression ________________________________________________ y=mx+b That is, when you graph T vs. J? , you should get a straight line with: y-intercept of zero; and 2_rr a slope of: J; = m (Eqn 2) So; from ygg data. determine the period T, for each change in length I. Set up your ordered pair as T vs. and graph. Calculate the slope and rearrange [351119) to determine 9. Complete the following Table based on your results: Length Length Frequency Period L Vi f T 100cm=1.00m 10cm=1m 0.47 Hz 2.13 seconds 80cm=0.8m 08.94cm=0.89m 0.55 Hz 1.81 seconds 60cm=0.6m 07.75cm=0.77m 0.54 HZ 1.68 seconds 40cm=0.4m 6.32cm=0.63m 0.76 Hz 1.32 seconds 20cm=0.2m 4.47cm=0.45m 0.99 Hz 1.01 seconds 2. Graph Period versus vLength - ( Tvs VI )3. What is the Slope of your line of best fit.4. 5. Use Eqn 2 and calculate the acceleration due to Gravity constant g' . Determine the percent error in your solution. high value - low value %error = x 100% average value