Physics with Calculus II

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Physics with Calculus II
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Where weve been

• Mechanics
• The Electric Field
• Electric Potential (V)
• DC Circuits
• Magnetic Field
• Induction
• Inductance
• ac circuits

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Ch 15 Introduction
Motion that repeats itself is very common and
applies to rotation, to oscillating springs, to
vibrating reeds, to waves as well as to many
other phenomena. Whenever there is a net
restoring force back to equilibrium for
displacement, we get oscillatory motion of one
type or another. The oscillations can be simple
(without change), with diminished amplitudes
(damping forces are present), increase amplitudes
(resonance phenomenon in forced oscillations),
and variations such as coupled oscillations, etc.
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Where were going
Ch 15 Oscillatory Motion (15.1) Motion of
Object on Spring (15.2) Math view of Simple
Harmonic Motion (15.3) Energy of Simple Harmonic
Oscillator (15.4) Comparing Simple Harmonic
Motion w/Uniform Circular Motion
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(15.1) Motion of Object on Spring
Resulting from force ? displacement from
equilibrium. If force acts toward the
equilibrium position, a repetitive back-and-forth
motion results. Examples molecules in
solid e.m. waves ac circuit
pendulum Forced oscillations replace lost
energy
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(15.1) Motion of Object on Spring
A particle moving in x direction (horizontal
spring/mass system). Figure 15.1
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(15.1) Motion of Object on Spring
A particle moving in x direction (horizontal
spring/mass system). Figure 15.1

• A ? max Amplitude
• ? angular frequency
• ? phase constant, (shift, angle)
• t ? time
• T ? period

SHM Demo Problem 13.1
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(15.2) The Block-Spring System, again

• Hookes Law from chapter 7
• F - k x ? linear restoring force
• More notes

Problem 13.9
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(15.3) Energy of Simple Harmonic Oscillator
Without friction, energy is conserved, so
Simplified
Problem 13-19 P 13.21
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(15.3) Energy of Simple Harmonic Oscillator
Figure 13.9
Problem I.P. 13.21
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• The End