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 14 Oscillations 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

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

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.special B.positive C.resonant D.damped E.pendulum Slide 14-6

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

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 Slide 14-4

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Equilibrium and Oscillation Slide 14-8

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

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

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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Sinusoidal Relationships Slide 14-10

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Mathematical Description of Simple Harmonic Motion Slide 14-11

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

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

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Solving Problems Slide 14-14