\f6. To investigate how the period depends on the length of the pendulum, using the data from Table 1, creat graphs of : period versus length, . period squared versus length period versus length squared. Use MS Excel to create the graphs. Make sure to display the equations on the graphs. On which one of these graphs do the data fall on a relatively straight line? What does this say about the relationship between the period and the length of the pendulum? Have your instructor check your graphs before leaving the lab. 7 compare exp, and theoretical gravity Using the following: T = 2 TTVI Slope = 4 TT ( of T ? VS. 9 ) g T 2 = ( 4 71 - )1 9 = 4 TT 2 9 (exp. g ) Slope 8 ) Find the lo error ( 9 = 9.8 m/s ? ) a Expl - the X 100 % 1016 - 98- 6:36 - 0.0367 x 100 theor 918 918 = 3.6701 Simple Harmonic MotionDATA TABLES Data Table 1: Varying Length Angular Amplitude = 10 Mass of Sphere = 46 . 97 - 8 Length (m) Str 10 Periods (s) 1 Period (s) 1020 20,44 4: 17 1: 10 20.5 5 2: 05 5 2 4. 2 2 1.00 20.414 190 2 040 2 180 17. 38 1. 7382 3. 0 2 1 1 170 15. 80 1 1 58 2 2: 49 6 Data Table 2: Varying Amplitude Length of pendulum = 100 cm Mass of sphere = 6 6.97 8 Angle () 10 Periods (s) 1 Period (s) 15 20. 38 2.038 13 19. 82 1 . 9 82 19. 36 1. 936 9 18. 66 1.966 18. 09 1. 809 4 1 2 = 10. 16 1.4114 5 141 . 14 3.8853 Simple Harmonic MotionData Table 3: Varying Mass Angular Amplitude = 10 Length of pendulum = 100 _cm Mass (g) 10 Periods (s) 1 Period (s) 67 . 32 19. 18 1. 918 4 2- 43 19.59 1 . 95 9 40- 73 20, 25 2. 025 20. 45 19. 22 1 . 9 2 2 Questions 1. Does the value of the period change as the length of the pendulum changes? How do you know? 2. Does the value of the period change as the mass of the sphere is changed? How do you know? 3. Does the value of the period change as the amplitude changes? How do you know? 4. From an error (accuracy) point of view, why should you measure 10 periods and divide by 10 to get the period rather than just directly measuring a single period? 5. If you took your pendulum to the moon, where the acceleration due to gravity is one sixth that on Earth, would you expect the period to be longer, shorter, or the same as on Earth? Why? 6. Describe how a pendulum might be used to keep time. 4 Simple Harmonic Motion