Equilibrium, restoring forces, and oscillation Mathematical description of oscillatory motion
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ht © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. • Equilibrium, restoring forces, and oscillation • Mathematical description of oscillatory motion • Energy in oscillatory motion • Damped oscillations • Resonance Chapter 14 Oscillations Topics: Slide 14-1
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Chapter 14 Oscillations. Equilibrium, restoring forces, and oscillation Mathematical description of oscillatory motion Energy in oscillatory motion Damped oscillations Resonance. Topics:. Slide 14-1. Reading Quiz. - PowerPoint PPT Presentation
Transcript of Equilibrium, restoring forces, and oscillation Mathematical description of oscillatory motion
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
• Equilibrium, restoring forces, and oscillation
• Mathematical description of oscillatory motion
• Energy in oscillatory motion
• Damped oscillations
• Resonance
Chapter 14Oscillations
Topics:
Slide 14-1
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Reading Quiz
2. A mass is bobbing up and down on a spring. If you increase the amplitude of the motion, how does this affect the time for one oscillation?A. The time increases.B. The time decreases.C. The time does not change.
Slide 14-4
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2. A mass is bobbing up and down on a spring. If you increase the amplitude of the motion, how does this affect the time for one oscillation?
C. The time does not change.
Slide 14-5
Answer
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Reading Quiz
3. If you drive an oscillator, it will have the largest amplitude if you drive it at its _______ frequency.A. specialB. positiveC. resonantD. dampedE. pendulum
Slide 14-6
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3. If you drive an oscillator, it will have the largest amplitude if you drive it at its _______ frequency.
C. resonant
Slide 14-7
Answer
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Review of Springs
Spring Force
Spring Potential Energy
Motion of spring and mass is sinusoidal
Physics Springs Assumption - ideal spring• Spring is massless• Spring stretch can be described by Hooke’s law for all
stretches and compressions• Neglect effect of spring coils in compression
Slide 14-4
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Equilibrium and Oscillation
Slide 14-8
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Linear Restoring Forces and Simple Harmonic Motion
If the restoring force is a linear function of the displacement from equilibrium, the oscillation is sinusoidal—simple harmonic motion.
Slide 14-9
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Describing periodic motion
CycleOne complete motion
PeriodTime for one cycle.Units of time - think of units as time per cycle
FrequencyCycles per unit timeUnit - cycles per second => Hertz (Hz)
Slide 14-4
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Describing oscillations
An object makes 10 completes oscillations (10 cycles) in 2 seconds.
a. How long does each oscillation take?
b. What is the frequency of revolutions?
Slide 14-4
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Sinusoidal Relationships
Slide 14-10
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Mathematical Description of Simple Harmonic Motion
Slide 14-11
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Energy in Simple Harmonic Motion
As a mass on a spring goes through its cycle of oscillation, energy is transformed from potential to kinetic and back to potential.
Slide 14-12
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Frequency and Period
The frequency of oscillation depends on physical properties of the oscillator; it does not depend on the amplitude of the oscillation.
Slide 14-13
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Solving Problems
Slide 14-14
