YouTube - Color Footage of Tacoma Narrows
YouTube - Tacoma Narrows Bridge Collapse
"Gallopin' Gertie"

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Motion reoccurs in a regular pattern
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Simple harmonic motion (SHM): force that restores the object to equilibrium is directly proportional to the displacement
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Two important measurements:
 Period (T): time to repeat one complete cycle
 Amplitude: maximum displacement

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Hooke's Law: force exerted by a spring is directly proportional to the amount the spring is stretched
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F = -kx
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PE=(1/2)kx 2
 http://web.hep.uiuc.edu/home/mats/WCIA/wcia_
030430_1.wmv

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Masses & Springs 2.02

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A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from the end. What is the spring constant?
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Known: x=0.18m F=56N
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F=-kx so k=F/x (the negative just means it's a restoring force)
 k=56N/0.18m = 310 N/m

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How much PE is stored in the spring?
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PE=(1/2)kx 2
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PE=(1/2)(310N/m)(0.18m) 2
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PE=5 J

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A 560 N bicyclist sits on a bicycle seat and compresses the two springs that hold it up. The spring constant is 2.2 x 10 4 N/m for each spring.
How much is each spring compressed?
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Know: F=560 N k=2.2 x 10 4 N/m 2 springs
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F=-kx or x=F/k and since 2 springs x=F/2k
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X=1.3 x 10 -2 m

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
Mass attached to a spring exhibits simple harmonic motion
T= 2 π√(m/k)
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Frequency is inverse of period!

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Object (bob) suspended by a string of length l
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String exerts tension (force) and gravity exerts force
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Period of a pendulum: T=2 π√(l/g)

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A pendulum with length 36.9 cm has a period of
1.22 s. What is the acceleration of gravity at the pendulum's location?
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Known: T=1.22 s l=0.369 m
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T=2 π√l/g so g=(2π) 2 l
(T) 2
 g=9.78 m/s 2