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Equilibrium, restoring forces, and oscillation Mathematical description of oscillatory motion

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.

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Equilibrium, restoring forces, and oscillation Mathematical description of oscillatory motion

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  1. Chapter 14 Oscillations • Equilibrium, restoring forces, and oscillation • Mathematical description of oscillatory motion • Energy in oscillatory motion • Damped oscillations • Resonance Topics: Slide 14-1

  2. Reading Quiz • 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? • The time increases. • The time decreases. • The time does not change. Slide 14-4

  3. Answer • 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? • The time does not change. Slide 14-5

  4. Reading Quiz • If you drive an oscillator, it will have the largest amplitude if you drive it at its _______ frequency. • special • positive • resonant • damped • pendulum Slide 14-6

  5. Answer • If you drive an oscillator, it will have the largest amplitude if you drive it at its _______ frequency. • resonant Slide 14-7

  6. 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

  7. Equilibrium and Oscillation Slide 14-8

  8. 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

  9. Describing periodic motion Cycle One complete motion Period Time for one cycle. Units of time - think of units as time per cycle Frequency Cycles per unit time Unit - cycles per second => Hertz (Hz) Slide 14-4

  10. Describing oscillations • An object makes 10 completes oscillations (10 cycles) in 2 seconds. • How long does each oscillation take? • What is the frequency of revolutions? Slide 14-4

  11. Sinusoidal Relationships Slide 14-10

  12. Mathematical Description of Simple Harmonic Motion Slide 14-11

  13. 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

  14. 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

  15. Solving Problems Slide 14-14

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