1. Foundations of Physics
CPO Science
Foundations of Physics
Unit 5, Chapter 13

2. Chapter 13 Harmonic Motion
Unit 5: Waves and Sound
Chapter 13 Harmonic Motion
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
harmonic motion
cycle
period
frequency
amplitude
hertz (Hz)
damping
periodic motion
periodic force
resonance
phase
phase difference
equilibrium
restoring force
stable equilibrium
unstable equilibrium
oscillator
natural frequency
steady state
piezoelectric effect

5. 13.1 Harmonic motion Key Question:
How do we describe the back and forth motion of a pendulum?
*Students read Section AFTER Investigation 13.1

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

7. 13.1 Harmonic motion is common
communications
sound
clocks
nature

9. 13.1 Amplitude
Amplitude describes the size of a cycle.

10. 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.

11. 13.1 Linear Motion vs. Harmonic Motion Graphs

13. 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.

14. 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.

15. 13.2 Why Things Oscillate Key Question:
What kinds of systems oscillate?
*Students read Section AFTER Investigation 13.2

16. 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.

17. 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.

18. 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).

19. 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.

20. 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.

21. 13.3 Resonance and Energy Key Question:
What is resonance and why is it important?
1. The restoring force pulls the pendulum toward the center (equilibrium).
2. The pendulum overshoots the center because of its inertia.
3. The restoring force pulls back toward the center, slowing and reversing the pendulum’s direction.
4. The pendulum overshoots the center again, because of inertia.
5. The cycle repeats, creating harmonic motion.
*Students read Section AFTER Investigation 13.3

22. 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.

23. 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.

24. 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.

25. Application: Quartz Crystals