29 - Pulses & Waves

# 29 - Pulses & Waves - Pulses and waves For next time...

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Pulses and waves For next time: Read: Chapter 16, sections 4-6 Homework: chapter 15, problems 22, 32, & 62

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Damped harmonic motion How can we take the damping force into account? dx b dt =− damping F bv Hence, the equation of motion becomes: 2 2 0 dx d x mb k x dt dt + +=
Damped harmonic motion 2 2 0 dx d x mb k x dt dt ++ = Make an educated guess at the solution ( ) cos with , , constants t xt A e t A α ω αω = Plug this “ansatz” back into the equation of motion and determine the constants

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Damped harmonic motion 2 2 , 24 bk b mm m αω == Solution: () 2 2 2 cos 4 b t m kb xt A e t ⎛⎞ =− ⎜⎟ ⎝⎠ 2 2 1 22 4 f ω ππ The larger b the quicker oscillations damp out
Damped harmonic motion () 2 2 2 cos 4 b t m kb xt A e t mm ⎛⎞ =− ⎜⎟ ⎝⎠ 2 2 2 A - underdamped 4 B - critically damped 4 C - overdamped 4 bm k k k < = >> 3 cases for heavily damped systems:

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Resonance http://physics.bu.edu/~duffy/semester1/c19_driven_sim.html driving force driving force
VD 9-3 "Driven spring and weight"

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Collapse of the Tacoma Narrows Bridge
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29 - Pulses & Waves - Pulses and waves For next time...

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