Graded Assignment Name: MTH403B: Pre-Calculus/Trigonometry | Unit 3 | 3.3 Checkup Date: Graded Assignment Checkup: Modeling Simple Harmonic Motion Answer the following questions using what you've learned from this lesson. Write your responses in the space provided and turn the assignment in to your instructor. 1. What is the period and frequency of a 10-pound weight oscillating (as a pendulum) on a 5meter-long rope? Score Answer: 2. A simple pendulum has a period of 15 seconds. What is the length of the pendulum in meters? Score Answer: For questions 3 - 6, consider the following situation. A mass oscillating up and down while attached to the bottom of a spring can be modeled using simple harmonic motion. If the weight is displaced from its equilibrium position a maximum of 7 centimeters and it takes 3 seconds to complete one cycle, answer the following questions: 3. What is the amplitude of the modeling function? Score Answer: 4. What is the period of the modeling function? Score Answer: 5. What is the frequency of the weight? Score Answer: 6. Write a possible equation of the modeling function. Score Answer: For questions 7 - 8, consider the following: A point on the tip of a tuning fork vibrates in harmonic motion described by the equation d 10 sin(t ) . 7. for a tuning fork that has a frequency of 535 vibrations per second. Score Answer: 8. How many cycles does the fork complete in 1 minute? 2009 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Score Page 1 of 3 Graded Assignment MTH403B: Pre-Calculus/Trigonometry | Unit 3 | 3.3 Checkup Answer: 3 t , answer the following questions: 4 Given the equation for simple harmonic motion d 1.3cos 9. Find the maximum displacement. Score Answer: 10. Find the frequency and length of the pendulum. Score Answer: 11. Calculate the value of d when t 3 . Score Answer: 12. Determine the least positive value of t for which d 0 . Score Answer: Given the equation for simple harmonic motion d 1 sin 60 t , answer the following questions: 12 13. Find the maximum displacement from equilibrium position. Score Answer: 14. Find the frequency. Score Answer: 15. Calculate the value of d when t 3 . Score Answer: 16. Determine the least positive value of t for which d 0 . Score Answer: 2009 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 2 of 3 Graded Assignment MTH403B: Pre-Calculus/Trigonometry | Unit 3 | 3.3 Checkup For questions 17 - 20, consider the following situation. A buoy oscillates in simple harmonic motion according to the motion of waves at sea. An observer notes that the buoy moves a total of 6 feet from its lowest point to its highest point. The buoy returns to its highest point every 15 seconds. 17. What is the amplitude of the function that models the buoy's motion? Score Answer: 18. What is the period of the function that models the buoy's motion? Score Answer: 19. What is the frequency of the buoy? Score Answer: 20. Write a possible equation that models the motion of the buoy. Score Answer: Your Score 2009 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. ___ of 10 Page 3 of 3