Name: Partner: Date: 10 Simple Harmonic Motion Introduction Simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement. It can serve as a mathematical model for a variety of motions, such as the oscillation of a spring (remember Hooke's Law?). Other phenomena can be approximated by simple harmonic motion, from the oscillation of a simple pendulum to molecular vibration. A simple pendulum motion can be described as simple harmonic motion provided the displacement angle is small, less than 10. The simple pendulum was one of the first timekeeping devices ever made. It was discovered long ago that the time for a pendulum to swing back and forth is always the same, i.e. its period is constant. For a simple pendulum, the period T is given by where L is the length of the pendulum (from the pivot point to the center of mass of the bob) and g is the acceleration due to gravity. Pre-lab and Discussion Questions Pre-Lab Questions This part of the lab is to be completed prior to class. You MUST show it to your instructor upon arrival or else no credit will be given for this section. 1. Define period in your own words: [5 pts] 2. How can you increase the frequency of a simple pendulum? Explain. [5 pts] 77Discussion Questions This part of the lab is to be completed with your group in class. 3. Draw a free-body diagram for the pendulum shown in the figure above. [5 pts] 4. Show that at small angles the restoring force is proportional to the displacement. (Hint - at small angles, sin 0 ~ 0 and cos 0 ~ 1) [5 pts] 5. Explain how you can determine the period of a pendulum without having a large measurement error. [5 pts] 78O wavel TO The waves describe O O D O O On OOC DO O 5. Calculate the percent error between the experimental value of g you obtained and the known (theoretical) value of g and record it in Data Table 2. Show your calculation. [5 pts] O Data Table 2: Comparison of accelerations [5 pts] gexpt m/ S'|9theory |9.8 m/ s2|% Error . Be sure to turn off the interface and tidy your station for the next class. Application Question 6. You want to create a basic timekeeping pendulum. You have a long piece of string, a 100 g mass, and a place to hang it. If you want the pendulum to take 2 seconds to swing from one side to the other, how much string must you use for hanging? [10 pts] 81