1. Physics 121C - Mechanics Lecture 23 (Knight: 14.1 - 14.6) Simple Harmonic Motion December 7, 2005 (29 Slides) John G. Cramer Professor of Physics B451 PAB cramer@phys.washington.edu

2. December 7, 2005Physics 121C - Lecture 232 Announcements Tycho is Fixed! Homework Assignment #9 is due on Midnight on Friday, December 9. Tycho Survey: Please complete the “Survey” in the Homework section of Tycho as soon as possible. Its completion is required for this course. The Final Exam will be held in this room on Monday, December 12 at 8:30 AM (Note: NOT 10:30 AM!). Exam #3 will be returned on Friday. The Exam 3 grades and solutions are now on the web. If your Exam 3 scores are missing, see Laura Clement (C136 PAB). Exam #3 regrade requests will be accepted until noon on Monday, December 12.

3. December 7, 2005Physics 121C - Lecture 233 Exam 3 Statistics Average = 57.83 Std Dev = 13.91 1.72.7 3.7 High = 88 Median = 58 Low = 14

4. December 7, 2005Physics 121C - Lecture 234 11 5-Dec-05 22 3-D Rotation, PrecessionSupplemental Angular Momentum Make-up labs 7-Dec-05 23 Simple Harmonic Motion 14.1 to 14.6 9-Dec-05 R4 Review & Extension - 12-Dec-05 FE FINAL EXAMINATION: Monday, December 12, 8:30 to 10:20 AM Lecture Schedule (Part 4) We are here!

5. December 7, 2005Physics 121C - Lecture 235 Oscillations Oscillations (whether sinusoidal or otherwise) have some common characteristics: 1.They take place around an equilibrium position; 2.The motion is periodic and repeats with each cycle.

6. December 7, 2005Physics 121C - Lecture 236 Frequency and Period

7. December 7, 2005Physics 121C - Lecture 237 Example: Radio Station Frequency and Period What is the oscillation period of an FM radio station that broadcasts at 100 MHz? Note that 1/Hz = s

8. December 7, 2005Physics 121C - Lecture 238 Simple Harmonic Motion The special case of an oscillation that has smooth sinusiodal motion is called “Simple Harmonic Motion”, abbreviated SHM. The motion can be described by a period (the time required for one complete oscillation) and an amplitude (the distance from the equilibrium position to a turning point). An example is a glider attached to a spring and moving on an air track.

9. December 7, 2005Physics 121C - Lecture 239 Kinematics of Simple Harmonic Motion

10. December 7, 2005Physics 121C - Lecture 2310 Example: A System in SHM An air-track glider is attached to a spring, pulled 20 cm to the right, and released at t-=0. It makes 15 complete oscillations in 10 s. a.What is the period of oscillation? b.What is the object’s maximum speed? c.What is its position and velocity at t=0.80 s?

11. December 7, 2005Physics 121C - Lecture 2311 Example: Finding the Time A mass, oscillating in simple harmonic motion, starts at x=A and has period T. At what time, as a fraction of T, does the mass first pass through x=½A?

12. December 7, 2005Physics 121C - Lecture 2312 SHM and Circular Motion Uniform circular motion projected into one dimension is simple harmonic motion.

13. December 7, 2005Physics 121C - Lecture 2313 SHM and Circular Motion

14. December 7, 2005Physics 121C - Lecture 2314 The Phase Constant  0

15. December 7, 2005Physics 121C - Lecture 2315 The Phase Constant  0

16. December 7, 2005Physics 121C - Lecture 2316 Example: Using Initial Conditions A mass on a spring oscillates with a period of 0.80 s and an amplitude of 10 cm. At t=0 s it is 5.0 cm to the left of equilibrium and moving to the left. What are its position and direction of motion at t=2.0 s?

17. December 7, 2005Physics 121C - Lecture 2317 Clicker Question 1 Shown are four harmonic oscillators at t=0. All are oscillating with amplitude A as shown. Their velocity directions are shown by the green arrows. Which one has the phase constant    ?

18. December 7, 2005Physics 121C - Lecture 2318 Energy and SHM

19. December 7, 2005Physics 121C - Lecture 2319 Energy and SHM

20. December 7, 2005Physics 121C - Lecture 2320 Example: Using Conservation of Energy A 500 g block on a spring is pulled a distance of 20 cm and released. The subsequent oscillations are measured to have a period of 0.80 s. At what position (or positions) is the speed of the block 1.0 m/s?

21. December 7, 2005Physics 121C - Lecture 2321 Clicker Question 2 Four springs have been compressed from their equilibrium positions at x=0 cm. Which system has the largest maximum speed in its oscillation?

22. December 7, 2005Physics 121C - Lecture 2322 The Dynamics of SHM

23. December 7, 2005Physics 121C - Lecture 2323 The Dynamics of SHM

24. December 7, 2005Physics 121C - Lecture 2324 The Equation of Motion

25. December 7, 2005Physics 121C - Lecture 2325 Solving the SHM Equation of Motion What is x? Let’s make a wild guess:

26. December 7, 2005Physics 121C - Lecture 2326 Example: Analyzing an Oscillator At t=0, a 500 g block oscillating on a spring is observed to be moving to the right at x=15 cm. It reaches a maximum displacement of 25 cm at t=0.300s. a.Draw a position vs. time graph for one cycle of motion. b.At what times during the cycle will the mass pass through 20 cm?

27. December 7, 2005Physics 121C - Lecture 2327 Vertical Oscillations

28. December 7, 2005Physics 121C - Lecture 2328 Vertical Oscillations

29. December 7, 2005Physics 121C - Lecture 2329 Example: A Vertical Oscillation A 200 g block hangs from a spring with spring constant 10 N/m. The block is pulled down to a point where the spring is 30 cm longer than it’s unstretched length, then released. Where is the block and what is its velocity 3.0 s later?

30. December 7, 2005Physics 121C - Lecture 2330 End of Lecture 23 Tycho is Fixed! Homework Assignment #9 is due on Midnight on Friday, December 9. Tycho Survey: Please complete the “Survey” in the Homework section of Tycho as soon as possible. The Final Exam will be held in this room on Monday, December 12 at 8:30 AM (Note: NOT 10:30 AM!). Exam #3 should be graded and returned by Friday. The Exam 3 solutions are on the web. Exam #3 regrade requests will be accepted until noon on Monday, December 12.