ENME361 Quiz 12 Solution

ENME361 Quiz 12 Solution - ENME 361 Fall 2008 Solution for...

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ENME 361 Fall 2008 Solution for Quiz #12 (December 4, 2008; Duration: 20 minutes) 1. Consider the spring-mass-damper prototype shown in the figure below. Given that the forced response of a linear, underdamped vibratory system can be determined from find the response of the system for the impulse forcing . Solution : By using the given response for x ( t ), we get the response for the given forcing f ( t ) as () 00 0 0 0 2 2 0 11 ( ) sin( ) ( ) sin( [ ]) ( ) sin( [ ]) ( ) sin( [ ]) ( ) n n n n tt t dd t t d d t t d d x te f t d e t f d mm f et t d m f t d m ζω η ζω η ω ηη ωω ωη δ −− =− = +− ∫∫ 0 2 0 2 22 sin( [ ]) ( ) sin( [ ]) ( ) n n f f e tt u e . 2. The governing equations of a two-degree-of-freedom system undergoing rotational motions are given by the following: 1 1 2 2 10 1 0 01 1 0 KK θ ⎧⎫ ⎡⎤ += ⎬⎨ ⎢⎥ −+ ⎣⎦ ⎩⎭ ±± Determine the system natural frequencies and mode shapes.
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This note was uploaded on 02/13/2011 for the course ENME 361 taught by Professor Yoo during the Spring '11 term at Maryland.

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ENME361 Quiz 12 Solution - ENME 361 Fall 2008 Solution for...

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