1. Foundations of Physics
CPO Science
Foundations of Physics
Unit 5, Chapter 19

2. Why do some objects move back and forth around an equilibrium position while others don’t?
Your answer
Reasoning

3. Chapter 19 Harmonic Motion
Unit 5: Waves and Sound
Chapter 19 Harmonic Motion
19.1 Harmonic Motion
19.2 Why Things Oscillate
19.3 Resonance and Energy

4. Chapter 19 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.

5. Chapter 19 Vocabulary Terms
harmonic motion
cycle
period
frequency
amplitude
hertz (Hz)
damping
periodic force
Resonance
oscillator
phase
phase difference
equilibrium
restoring force
natural frequency
steady state

6. 19.1 Harmonic motion Key Question:
How do we describe the back and forth motion of a pendulum?
*Students read Section AFTER Investigation 13.1

7. What is Harmonic Motion?
communications
sound
clocks
nature

8. Harmonic motion is any motion that repeats

9. Oscillation
“I oscillated between wearing a green shirt and a blue shirt.”
Oscillate: to go back and forth
Oscillation: a motion that repeats regularly
Oscillator: something that goes back and forth; starts at a position and returns to it over and over. A pendulum is an oscillator.
Vibration: a fast oscillation

10. Cycles, systems, and oscillators
A cycle is the unit of motion that repeats as an oscillator moves.
What are some other CYCLES you can think of?

11. Period v Frequency Seconds/cycle Cycles/second
Period: the time it takes to complete one cycle; measured in SECONDS
Seconds/cycle
Frequency: how many cycles can occur in one second; measured in HERTZ
Cycles/second

12. Period v Frequency
Period refers to the time it takes something to happen.
Frequency refers to how often something happens.
Frequency is a rate quantity. Period is a time quantity.

14. Amplitude describes the size of a cycle.
how far from equilibrium the object moves.

15. How does energy relate to amplitude?

16. 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.

17. 19.1 Summary:
Harmonic motion is different from linear motion because it repeats. An oscillator is something that repeats a motion called an oscillation. The motion that repeats is called the cycle. The time it takes for one cycle is the period; the number of cycles that can occur in a second is the frequency, which is measured in hertz.

18. What do you know? Draw an original representation of harmonic motion.
Explain how the terms you learned relate directly to your drawing
Create a concept map of the terms you learned (a representation of how they are related)

20. 19.2 Linear Motion vs. Harmonic Motion Graphs

22. 19.2 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.

23. 19.2 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.

24. Video clip
2:50 – 3:10

25. 19.3 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.

26. 19.3 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 net force.

27. 19.3 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).
Systems in harmonic motion must have a restoring force

28. 19.3 The natural frequency
The natural frequency is the frequency at which a system tends to oscillate when disturbed.
Everything that can oscillate has a natural frequency and most systems have more than one.
It doesn’t matter how many times you set your pendulum in motion, or at what angle, it will have the same natural frequency (and therefore period)
Adding a steel nut greatly increases the inertia of a stretched rubber band, so the natural frequency decreases.

29. Can the natural frequency (or period) change?
Natural frequency depends on a balance between restoring force and inertia
Changing the mass changes the natural frequency ONLY if the restoring force is not due to gravity! This is because , just like free fall, the added inertia is equal to the added force from gravity. Gravity is independent of mass!

30. How do you change the natural frequency (or period) of a pendulum?
The natural frequency depends only on the length of the string.
Longer string means the restoring force is spread over a greater distance = longer period
The strings on a guitar are changed by varying the tension on the string

31. 19.3 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.

32. 19.3 Resonance and Energy
Resonance occurs when the periodic force has the same frequency as the natural frequency as the system. Energy is added at the right time, greater amplitude results.
When resonance occurs, the amplitude response is very large compared to the strength of the force applied

33. 19.3 Resonance
A good way to understand resonance is to think about three distinct parts of any interaction between a system and a force.

34. Examples of resonance Shattering wine glass
Force applied at the natural frequency, the amplitude builds up until it shatters
Swinging on swing set
you learn to “pump”, or push someone, at the natural frequency of the swing
amplitude of swing builds up = larger swing
Tacoma Narrows Bridge
Read page (hmmm, very interesting!)