1. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Lectures by James Pazun Chapter 13 Periodic Motion

2. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Describing oscillations The spring drives the glider back and forth on the air-track and you can observe the changes in the free-body diagram as the motion proceeds from –A to A and back. Refer to Example 13.1.

3. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Simple harmonic motion An ideal spring responds to stretch and compression linearly, obeying Hooke’s Law. For a real spring, Hookes’ Law is a good approximation.

4. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Simple harmonic motion viewed as a projection If you illuminate uniform circular motion (say by shining a flashlight on a candle placed on a rotating lazy-Susan spice rack), the shadow projection that will be cast will be undergoing simple harmonic motion.

5. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley X versus t for SHO then simple variations on a theme

6. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed v max ? A. T and v max both double. B. T remains the same and v max doubles. C. T and v max both remain the same. D. T doubles and v max remains the same. E. T remains the same and v max increases by a factor of. Q13.1

7. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed v max ? A. T and v max both double. B. T remains the same and v max doubles. C. T and v max both remain the same. D. T doubles and v max remains the same. E. T remains the same and v max increases by a factor of. A13.1

8. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley SHM phase, position, velocity, and acceleration SHM can occur with various phase angles. For a given phase we can examine position, velocity, and acceleration.

9. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an x-t graph for an object in simple harmonic motion. A. t = T/4 B. t = T/2 C. t = 3T/4 D. t = T Q13.2 At which of the following times does the object have the most negative velocity v x ?

10. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an x-t graph for an object in simple harmonic motion. A. t = T/4 B. t = T/2 C. t = 3T/4 D. t = T A13.2 At which of the following times does the object have the most negative velocity v x ?

11. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Watch variables change for a glider example As the glider undergoes SHM, you can track changes in velocity and acceleration as the position changes between the classical turning points. Refer to Problem- Solving Strategy 13.1 and Example 13.3.

12. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an x-t graph for an object in simple harmonic motion. A. t = T/4 B. t = T/2 C. t = 3T/4 D. t = T Q13.3 At which of the following times does the object have the most negative acceleration a x ?

13. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an x-t graph for an object in simple harmonic motion. A. t = T/4 B. t = T/2 C. t = 3T/4 D. t = T A13.3 At which of the following times does the object have the most negative acceleration a x ?

14. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an a x -t graph for an object in simple harmonic motion. A. t = 0.10 s B. t = 0.15 s C. t = 0.20 s D. t = 0.25 s Q13.5 At which of the following times does the object have the most negative velocity v x ?

15. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley This is an a x -t graph for an object in simple harmonic motion. A. t = 0.10 s B. t = 0.15 s C. t = 0.20 s D. t = 0.25 s A13.5 At which of the following times does the object have the most negative velocity v x ?

16. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Energy in SHM Energy is conserved during SHM and the forms (potential and kinetic) interconvert as the position of the object in motion changes.

17. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Energy in SHM II Figure 13.15 shows the interconversion of kinetic and potential energy with an energy versus position graphic. Refer to Problem-Solving Strategy 13.2. Follow Example 13.4.

18. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley A. t = T/8B. t = T/4 C. t = 3T/8D. t = T/2 E. more than one of the above This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. Q13.7 At which of the following times is the kinetic energy of the object the greatest?

19. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley A. t = T/8B. t = T/4 C. t = 3T/8D. t = T/2 E. more than one of the above This is an x-t graph for an object connected to a spring and moving in simple harmonic motion. A13.7 At which of the following times is the kinetic energy of the object the greatest?

20. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley To double the total energy of a mass-spring system oscillating in simple harmonic motion, the amplitude must increase by a factor of A. 4. B. C. 2. D. E. Q13.8

21. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley A. 4. B. C. 2. D. E. To double the total energy of a mass-spring system oscillating in simple harmonic motion, the amplitude must increase by a factor of A13.8

22. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Find velocity 1) What is the velocity as a function of the position v(x) for a SHO glider with mass m and spring constant k? Use conservation of energy 2) What is the maximum velocity of the glider?

23. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vibrations of molecules Two atoms separated by their internuclear distance r can be pondered as two balls on a spring. The potential energy of such a model is constructed many different ways. The Leonard–Jones potential shown as Equation 13.25 is sketched in Figure 13.20 below. The atoms on a molecule vibrate as shown in Example 13.7.

24. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Old car The shock absorbers in my 1989 Mazda with mass 1000 kg are completely worn out (true). When a 980-N person climbs slowly into the car, the car sinks 2.8 cm. When the car with the person aboard hits a bump, the car starts oscillating in SHM. Find the period and frequency of oscillation. How big of a bump (amplitude of oscillation) before you fly up out of your seat?

25. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Damped oscillations A person may not wish for the object they study to remain in SHM. Consider shock absorbers and your automobile. Without damping the oscillation, hitting a pothole would set your car into SHM on the springs that support it.

26. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Damped oscillations II

27. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Forced (driven) oscillations and resonance A force applied “in synch” with a motion already in progress will resonate and add energy to the oscillation (refer to Figure 13.28). A singer can shatter a glass with a pure tone in tune with the natural “ring” of a thin wine glass.

28. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Forced (driven) oscillations and resonance II The Tacoma Narrows Bridge suffered spectacular structural failure after absorbing too much resonant energy (refer to Figure 13.29).