Ch3-1 - Chile Mine Rescue Operation Chapter 3 General...

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Chile Mine Rescue Operation
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Chapter 3: General Forced Response In the topics covered so far, all of the driving forces have been harmonic excitation, i.e., sine or cosine excitations Linear combination of harmonic excitation has been also used. Here we examine the response to any form of excitation such as: Impulse Sums of harmonic functions: sines and cosines Any (integrable) function 2 1:20:36 00 11 0 ( ) ( ) ( ) cos mx t cx t kx t F t + + = cos( ) + sin( ) harmonic forcing functions mx cx kx c Y t kY t
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Review: Linear Superposition Principle 1 2 1 1 2 2 If ( ) and (t) are solutions of a linear homogeneous equation of motion, then ( ) ( ) (t) is also a solution to the same equation of motions. x t x x t a x t a x This principle allows us to break up complicated forces into sums of simpler forces, compute the response and add to get the total solution 2 1 1 2 2 2 2 1 2 1 2 If ( ) is the particular solution of ( ) and ( ) is for ( ) ( ) ( ) ( ) solves ( ) ( ) n n n x t x x f t x t x x f t x t ax t bx t x x a f t b f t 3 10:37:07 00 02
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