Physics 2111, 2008 Fundamentals of Physics 1 Fundamentals of Physics Chapter 13 Oscillations 1. Oscillations 2. Simple Harmonic Motion Velocity of SHM Acceleration of SHM 3. The Force Law for SHM 4. Energy in SHM 5. An Angular Simple Harmonic Oscillator 6. Pendulums The Simple Pendulum The Physical Pendulum Measuring “g” 7. SHM & Uniform Circular Motion 8. Damped SHM 9. Forced Oscillations & Resonance
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Physics 2111, 2008 Fundamentals of Physics 1 Chapter 13 Oscillations 1.Oscillations 2.Simple Harmonic Motion Velocity of SHM Acceleration of SHM 3.The.
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Physics 2111, 2008 Fundamentals of Physics 1
Fundamentals of Physics
Chapter 13 Oscillations
1. Oscillations
2. Simple Harmonic Motion
Velocity of SHM
Acceleration of SHM
3. The Force Law for SHM
4. Energy in SHM
5. An Angular Simple Harmonic Oscillator
6. Pendulums
The Simple Pendulum
The Physical Pendulum
Measuring “g”
7. SHM & Uniform Circular Motion
8. Damped SHM
9. Forced Oscillations & Resonance
Physics 2111, 2008 Fundamentals of Physics 2
Oscillations
Oscillations - motions that repeat themselves.
Oscillation occurs when a system is disturbed from a position of stable equilibrium.
– Clock pendulums swing
– Boats bob up and down
– Guitar strings vibrate
– Diaphragms in speakers
– Quartz crystals in watches
– Air molecules
– Electrons
– Etc.
Physics 2111, 2008 Fundamentals of Physics 3
Oscillations
Oscillations - motions that repeat themselves.
Physics 2111, 2008 Fundamentals of Physics 4
Simple Harmonic Motion
Harmonic Motion - repeats itself at regular intervals (periodic).
Frequency - # of oscillations per second
1 oscillation / s = 1 hertz (Hz)
Period - time for one complete oscillation (one cycle)
T
T
Tf
1
Physics 2111, 2008 Fundamentals of Physics 5
Simple Harmonic Motion
Position T
ime
Physics 2111, 2008 Fundamentals of Physics 6
Simple Harmonic Motion
Angles are in radians.
2T
f 2
s
cyclescycle
radianss
radians
fT
1
Physics 2111, 2008 Fundamentals of Physics 7
Amplitude, Frequency & Phase
The frequency of SHM is independent of the amplitude.
txtx m cos
txtx m cos
txtx m 2cos
4cosmx t x t
m mx x
Physics 2111, 2008 Fundamentals of Physics 8
Velocity & Acceleration of SHM
In SHM, a(t) is proportional to x(t) but opposite in sign.
txtx m cos
txtv m sin
dt
dxtv
txta m cos2
txta 2
The phase of v(t) is shifted ¼ period relative to x(t),
mxv max
mxa 2max
dt
dvta
Physics 2111, 2008 Fundamentals of Physics 9
The Force Law for SHM
Simple Harmonic Motion is the motion executed by a particle of mass m subject to a force proportional to the displacement of the particle but opposite in sign.
“Linear Oscillator”: F ~ - x
F t k x t
SimpleHarmonicMotion/HorizSpring.html
Hooke’s Law:
Physics 2111, 2008 Fundamentals of Physics 10
The Differential Equation that Describes SHM
Simple Harmonic Motion is the motion executed by a particle of mass m subject to a force proportional to the displacement of the particle but opposite in sign. Hooke’s Law!
txktF
amF Newton’s 2nd Law:
The general solution of this differential equation is: