1. Topic 4: Oscillations & Waves

2. Introduction
All motion is either periodic or non-periodic. In periodic motion an object repeats its pattern of motion at a fixed interval of time: it is regular and repeated. Wave motion is also periodic and there are many similarities between oscillations and waves; in this topic we will consider the common features but also see that there are differences.

3. Objectives & Understandings
SWBAT
Qualitatively describe the energy changes taking place during one cycle of an oscillation
Sketch & interpret graphs of simple harmonic motion examples
Understand what is meant by simple harmonic motion (SHM) & its conditions
Understand and define the terms time period, frequency, amplitude, displacement, and phase difference.

4. Some Key Vocabulary
Wave - a disturbance that transfers energy (not matter) through a medium from one location to another location
Medium - a substance or material that carries the wave
Equilibrium position – the rest position; zero displacement
Amplitude – A - maximum value for the displacement
Frequency – f - number of oscillations per second
Period – T - time required for one complete oscillation
Angular frequency – ω - the magnitude of the vector quantity angular velocity (radians/second) 𝜔=2𝜋𝑓= 2𝜋 𝑇

5. Oscillations Isochronous oscillations – (Pronunciation: ī-ˈsä-krə-nəs)
The Latin breakdown: Iso (same) chronos (time)
repeat in the same time period
Describing periodic motion
Wavelength – λ - distance from crest to crest or trough to trough.
Also all the other vocabulary that we just discussed…

6. Practice In the diagram above, which letter refers to a wavelength?
In the diagram above, which letter refers the amplitude?

7. More Practice
What is the amplitude of each wave on the graph below? What is the wavelength?

8. Simple Harmonic Motion
Conditions – the magnitude of the acceleration is proportional to the displacement of the object from a fixed point and the direction is always towards that fixed point.
𝑎∝−𝑥;
Spring restoring force: F=-kx
Watch this video to view the x, v, and a graphs for an object undergoing simple harmonic motion
Watch this video to view the conservation of energy in simple harmonic motion
𝝎= 𝒌 𝒎 = 𝒈 𝑳

9. Graphs: Simple Harmonic Motion
Displacement, velocity & acceleration time graphs
Acceleration-displacement graph

10. Check for Understanding
During SHM, where would the object have the greatest displacement?
During SHM, where would the object have the greatest velocity?
During SHM, where would the object have the greatest acceleration?

11. Energy Changes in SHM Total energy remains constant (conserved)
Potential energy is a minimum at equilibrium & maximum at maximum displacement
Kinetic energy is a maximum at equilibrium & minimum at maximum displacement

12. Phase & phase difference
Phase difference - φ - the measure of how "in step" different particles are. If they are moving together they are said to be in phase. If not they are said to be out of phase.

13. Phase Difference continued
Example: the phase difference between the displacement and velocity graphs is T/4 or 90° or π/2 radians.
Period T = 360° = 2π radians
T/2 = 180° = π radians
T/4 = 90° = π/2 radians
What is the phase difference between displacement and acceleration?

14. Elaborate Wave Amplitude Medium Frequency Equilibrium Position Period
Create vocabulary tabs for the 10 “new” vocabulary terms listed below. Include a definition & picture. If applicable, include equations, units & symbols. Use at least 4 colors. Place the word on the front.
Wave
Amplitude
Medium
Frequency
Equilibrium Position
Period
Simple Harmonic Motion
Wavelength
Phase difference
Crest/Trough

15. Elaborate Try this problem set
Whiteboard one problem & present the solution to the class.