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: Question: The gibbon will swing more rapidly and move more quickly through the trees if it raises its feet. How can we model the gibbon’s motion to understand this observation? Answer: Think about a pendulum: Grandfather’s clock. The longer the arm (l) the longer the period (T) , the longer it takes for the arm to swing from one end to the other. T ~ l Slide 14-1
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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:
Question: The gibbon will swing more rapidly and move more quickly through the trees if it raises its feet. How can we model the gibbon’s motion to understand this observation? Answer: Think about a pendulum: Grandfather’s clock. The longer the arm (l) the longer the period (T) , the longer it takes for the arm to swing from one end to the other. T ~ l
Slide 14-1
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Heartbeat: Electrocardiogram Period/
Frequency
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Vibration of Eardrum
Amplitude/ Resonance
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Swing, Grandfather’s clock: Pendulum Systems
Amplitude: parametric resonance Period: Length and gravity
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Spring-Mass System�
Oscillation: Amplitude, Period / Frequency
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
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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.
Displacement, velocity and acceleration of SHM:
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