Transcript Topic 4: Oscillations & Waves

4.1 Oscillations
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.
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.
Some Key Vocabulary
 Wave - a disturbance that transfers energy (not matter)
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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
2𝜋
quantity angular velocity (radians/second) 𝜔 = 2𝜋𝑓 =
𝑇
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…
Practice
In the diagram above, which letter refers to a wavelength?
In the diagram above, which letter refers the amplitude?
More Practice
 What is the amplitude of each wave on the graph
below? What is the wavelength?
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; 𝑎 = −𝑘𝑥
 Restoring force: F=ma=-mkx
 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
Graphs: Simple Harmonic Motion
 Displacement, velocity &
acceleration time graphs
 Acceleration-displacement
graph
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?
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
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.
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?
Elaborate
 Create vocabulary tabs for the new vocabulary terms
listed below. Include a definition & picture. If
applicable, include equations, units & symbols.
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Wave
Medium
Equilibrium Position
Simple Harmonic
Motion
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Amplitude
Frequency
Period
Wavelength
Phase difference
Elaborate
 Try this problem set
 Whiteboard one problem & present the solution to the
class.