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YouTube - Color Footage of Tacoma Narrows YouTube - Tacoma Narrows Bridge Collapse "Gallopin' Gertie". Simple Harmonic Motion. Periodic Motion. Motion reoccurs in a regular pattern - PowerPoint PPT Presentation
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Simple Harmonic Motion
YouTube - Color Footage of Tacoma Narrows
YouTube - Tacoma Narrows Bridge Collapse "Gallopin' Gertie"
Periodic Motion
Motion reoccurs in a regular pattern Simple harmonic motion (SHM): force that
restores the object to equilibrium is directly proportional to the displacement
Two important measurements: Period (T): time to repeat one complete cycle Amplitude: maximum displacement
Mass on a Spring
Hooke's Law: force exerted by a spring is directly proportional to the amount the spring is stretched
F = -kx PE=(1/2)kx2
http://web.hep.uiuc.edu/home/mats/WCIA/wcia_030430_1.wmv
Springs!
Masses & Springs 2.02
Example
A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from the end. What is the spring constant?
Known: x=0.18m F=56N F=-kx so k=F/x (the negative just means it's a
restoring force) k=56N/0.18m = 310 N/m
Example Continued
How much PE is stored in the spring? PE=(1/2)kx2
PE=(1/2)(310N/m)(0.18m)2
PE=5 J
Now you try it!
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 104 N/m for each spring. How much is each spring compressed?
Know: F=560 N k=2.2 x 104 N/m 2 springs F=-kx or x=F/k and since 2 springs x=F/2k X=1.3 x 10-2 m
Period of a Spring
Mass attached to a spring exhibits simple harmonic motion
T= 2π√(m/k) Frequency is inverse of
period!
Pendulum
Object (bob) suspended by a string of length l String exerts tension (force) and gravity exerts
force Period of a pendulum: T=2π√(l/g)
Sample Problem
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?
Known: T=1.22 s l=0.369 m T=2π√l/g so g=(2π)2l
(T)2
g=9.78 m/s2
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