2. Chapter 13: Energy Flow and Power  13.1 Harmonic Motion  13.2 Why Things Oscillate  13.3 Resonance and Energy

3. Chapter 13 Objectives  Identify characteristics of harmonic motion, such as cycles, frequency, and amplitude.  Determine period, frequency, and amplitude from a graph of harmonic motion.  Use the concept of phase to compare the motion of two oscillators.  Describe the characteristics of a system that lead to harmonic motion.  Describe the meaning of natural frequency.  Identify ways to change the natural frequency of a system.  Explain harmonic motion in terms of potential and kinetic energy.  Describe the meaning of periodic force.  Explain the concept of resonance and give examples of resonance.

4. Chapter 13 Vocabulary Terms  amplitude  damping  frequency  harmonic motion  hertz (Hz)  natural frequency  oscillator  period  periodic force  periodic motion  phase  phase difference  piezoelectric effect  resonance  stable equilibrium  unstable equilibrium

5. Inv 13.1 Harmonic motion Investigation Key Question: How do we describe the back and forth motion of a pendulum?

6. 13.1 Cycles, systems, and oscillators A cycle is a unit of motion that repeats.

7. 13.1 Harmonic motion is common sound communications clocks nature

8. 13.1 Describing harmonic motion  The period of an oscillator is the time to complete one cycle.

9. 13.1 Describing harmonic motion  Frequency is closely related to period.  The frequency of an oscillator is the number of cycles it makes per second. At a frequency of 100 Hz, an oscillating rubber band completes 100 cycles per sec.

10. 13.1 Describing harmonic motion  The unit of one cycle per second is called a hertz (Hz).  When you tune into a station at 100.6 on the FM dial, you are setting the oscillator in your radio to a frequency of 100.6 megahertz (MHz).

11. 13.1 Amplitude  Amplitude describes the size of a cycle.  The value of the amplitude is the maximum amount the system moves away from equilibrium.

12. 13.1 Amplitude  The energy of an oscillator is proportional to the amplitude of the motion.  Friction drains energy away from motion and slows the pendulum down.  Damping is the term used to describe this loss.

13. 13.1 Harmonic Motion Graphs  Graphs of linear motion do not show cycles.

14. 13.1 Harmonic motion graphs  Graphs of harmonic motion repeat every period, just as the motion repeats every cycle.  Harmonic motion is sometimes called periodic motion.

15. 13.1 Circles and the phase of harmonic motion  Circular motion is very similar to harmonic motion.  Rotation is a cycle, just like harmonic motion.  One key difference is that cycles of circular motion always have a length of 360 degrees.

16. 13.1 Circles and the phase of harmonic motion  The word “phase” means where the oscillator is in the cycle.  The concept of phase is important when comparing one oscillator with another.

17. Chapter 13: Energy Flow and Power  13.1 Harmonic Motion  13.2 Why Things Oscillate  13.3 Resonance and Energy

18. Inv 13.2 Why Things Oscillate Investigation Key Question: What kinds of systems oscillate?

19. 13.2 Why Things Oscillate  Systems that have harmonic motion move back and forth around a central or equilibrium position.  Equilibrium is maintained by restoring forces.  A restoring force is any force that always acts to pull the system back toward equilibrium.

20. 13.2 Inertia  Newton’s first law explains why harmonic motion happens for moving objects.  According to the first law, an object in motion stays in motion unless acted upon by a force.

21. 13.2 Stable and unstable systems  Not all systems in equilibrium show harmonic motion when disturbed.  In unstable systems there are forces that act to pull the system away from equilibrium when disturbed.  Unstable systems do not usually result in harmonic motion (don't have restoring forces).

22. 13.2 The natural frequency  The natural frequency is the frequency at which systems tend to oscillate when disturbed.  Everything that can oscillate has a natural frequency, and most systems have more than one. Adding a steel nut greatly increases the inertia of a stretched rubber band, so the natural frequency decreases.

23. 13.2 Changing the natural frequency  The natural frequency is proportional to the acceleration of a system.  Newton’s second law can be applied to see the relationship between acceleration and natural frequency.

25. Chapter 13: Energy Flow and Power  13.1 Harmonic Motion  13.2 Why Things Oscillate  13.3 Resonance and Energy

26. Inv 13.3 Resonance and Energy Investigation Key Question: What is resonance and why is it important?

27. 13.3 Resonance and Energy  Harmonic motion involves both potential energy and kinetic energy.  Oscillators like a pendulum, or a mass on a spring, continually exchange energy back and forth between potential and kinetic.

28. 13.3 Resonance  A good way to understand resonance is to think about three distinct parts of any interaction between a system and a force.

29. 13.2 Resonance  Resonance occurs when the frequency of a periodic force matches the natural frequency of a system in harmonic motion.

30. 13.3 Energy, resonance and damping  Steady state is a balance between damping from friction and the strength of the applied force.  Dribbling a basketball on a floor is a good example of resonance with steady state balance between energy loss from damping and energy input from your hand.

31.  The precise heartbeat of nearly all modern electronics is a tiny quartz crystal oscillating at its natural frequency.  In 1880, Pierre Curie and his brother Jacques discovered that crystals could be made to oscillate by applying electricity to them.  This is known as the piezoelectric effect. Quartz Crystals