Not so Simple Harmonic Oscillator

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Not so SimpleHarmonic Oscillator

• Simple harmonic motion
• Damped harmonic motion
• Driven harmonic motion

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Reading Questions
This photograph is from the reading for today.

1. True
2. False

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Reading Questions
This photograph is from the reading for today.

1. True
2. False

4
Reading Questions
The photograph is illustrating

1. oscillations
2. damped oscillations
3. resonance
4. simple harmonic motion
5. None of the above

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Reading Questions
The photograph is illustrating

1. oscillations
2. damped oscillations
3. resonance
4. simple harmonic motion
5. None of the above

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Reading Questions
What term is used to describe an oscillator that
runs down and eventually stops?
1. Tired oscillator 2. Out of shape oscillator 3.
Damped Oscillator 4. Resonant oscillator 5.
Driven oscillator
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Reading Questions
What term is used to describe an oscillator that
runs down and eventually stops?
1. Tired oscillator 2. Out of shape oscillator 3.
Damped Oscillator 4. Resonant oscillator 5.
Driven oscillator
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Oscillatory Motion
Simple Harmonic Motion
Hooks law
Newtons law
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Oscillatory Motion
two constants of integration
angular frequency
T, f, w, scale in time A, scales in space f,
shifts in time D, shifts in space
f - p/2
f 0
f - p/4
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Class Questions
Four springs have been compressed from their
equilibrium position at x 0 cm. When released,
they will start to oscillate. Rank in order, from
highest to lowest, the maximum speeds of the
oscillators.
1. c gt b gt a d 2. c gt b gt a gt d 3. d gt a gt b gt
c 4. a d gt b gt c 5. b gt c gt a d
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Class Questions
Four springs have been compressed from their
equilibrium position at x 0 cm. When released,
they will start to oscillate. Rank in order, from
highest to lowest, the maximum speeds of the
oscillators.
1. c gt b gt a d 2. c gt b gt a gt d 3. d gt a gt b gt
c 4. a d gt b gt c 5. b gt c gt a d
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Class Questions
This is the position graph of a mass on a spring.
What can you say about the velocity and the force
at the instant indicated by the dotted line?
1. Velocity is positive force is to the
right. 2. Velocity is negative force is to the
left. 3. Velocity is negative force is to the
right. 4. Velocity is zero force is to the
right. 5. Velocity is zero force is to the left.
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Class Questions
This is the position graph of a mass on a spring.
What can you say about the velocity and the force
at the instant indicated by the dotted line?
1. Velocity is positive force is to the
right. 2. Velocity is negative force is to the
left. 3. Velocity is negative force is to the
right. 4. Velocity is zero force is to the
right. 5. Velocity is zero force is to the left.
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Oscillatory Motion
Energy
Is energy conserved?
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Oscillatory Motion
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Student Workbook
When the potential energy is zero the spring is
at its equilibrium position. 20 cm
A turning point is where the total energy is
equal to the potential energy. 18 and 26 cm.
The maximum kinetic energy is where the potential
energy is zero. 7 J
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Student Workbook
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Oscillatory Motion
Yes! There are two turning points so the
particle oscillates between the two turning
points.
No! The potential energy is a parabola for
simple harmonic motion.
3 cm.
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Oscillatory Motion
Damped Harmonic Motion
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Oscillatory Motion
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Student Workbook
more
more
decreased
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Student Workbook
So the period increases by the square root of 2.
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Student Workbook
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Class Question
Which damped oscillator has the smallest decay
time constant?
1. ta 2. tb 3. tc 4. td 5. All have the
same decay time constant
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Class Question
Which damped oscillator has the smallest decay
time constant?
1. ta 2. tb 3. tc 4. td 5. All have the
same decay time constant
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Oscillatory Motion
Driven Harmonic Oscillations and Resonance
Response Curve
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Oscillatory Motion
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Student Workbook
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Student Workbook
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Student Workbook
31
Oscillatory Motion
Resonance
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Oscillatory Motion
Resonance