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Review Exam 1
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Simple Harmonic Motion
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11-1 Simple Harmonic MotionThe force exerted by the spring depends on the displacement:
(11-1)
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11-2 Energy in the Simple Harmonic Oscillator
We already know that the potential energy of a spring is given by:
The total mechanical energy is then:
(11-3)
The total mechanical energy will be conserved, as we are assuming the system is frictionless.
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11-2 Energy in the Simple Harmonic Oscillator
The total energy is
And we can write:
(11-4c)
This can be solved for the velocity as a function of position:
(11-5)
where
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11-3 The Period and Sinusoidal Nature of SHM
(11-7a)
(11-7b)
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11-4 The Simple Pendulum
Therefore, for small angles, we have:
where
The period and frequency are:
(11-11a)
(11-11b)
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Harmonic Disturbance
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11-7 Wave Motion
Wave characteristics:
• Amplitude, A
• Wavelength, λ
• Frequency f and period T
• Wave velocity (11-12)
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Waves on a String
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lengthmass where
F
v
nd1,2,3,...an where
n2L
vf;
n
2Lλ
T
nn
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Guitar String
Why?
λ(sound)λ(string)but f(sound)f(string)
nd1,2,3,...an where
f n 2L
vf SOUNDSTRING
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1,2,3,...nfor n 2L
vf and
n
2Lλ sound
nn
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1,3,5,...nfor n 4L
vf and
n
4Lλ sound
nn
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Loud
Quiet
http://library.thinkquest.org/19537/cgi-bin/showharm.cgi#
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Both Source and Observer Moving
sourcesound
observersound
sound
source
sound
observer
'
v v
v v f
vv
1
vv
1
f f
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Exam• 5 problems • 3 Qualitative (30 points)• 2 Quantitative (70 points)• Suggestions– Read problem carefully– Underline important stuff, cross out extraneous stuff– Outline solution if out of time– If you think you need a quantity that doesn’t appear to
you to be there, make one up.– Study Equation Sheet.