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:

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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.

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Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

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

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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

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Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

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

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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.

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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)

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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?

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Sinusoidal Relationships

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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.

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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.

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Solving Problems

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