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Unformatted text preview: Name_________________________ Page 1 of 2 12/8/2005 (Fall 2000) The spring-mass-dashpot system shown to the right has been modeled to give ( / ) (1/ ) ( / ) (1/ ) out out out in in q R I q IC q R I q IC q + + = + dd d d where standard conversions between , , I C R and , , m k b have been made. Assuming m 4000 lb m = , a natural frequency of 10 radians per second and 5 percent critical damping. a. What is the stiffness k and damping constant b ? In one of the two standard forms per the left hand side of the system equation, one finds that the system equation can be rewritten as 2 2 2 2 out n out n out n in n in q q q q q ζω ω ζω ω + + = + dd d d . Thus 2 1/ / n IC k m ω = = and 2 / / n R I b m ζω = = . Therefore ( ) 2 2 3 2 m m 4000 lb 10 rad/s 400*10 lb /s n k m ω = = = and m m 2 2*.05*10rad/s*4000 lb 4000 lb /s n b m ζω = = = . Although both of these answers are technically correct neither answer is in standard units. Conversion to standard units requires multiplication by “1”,...
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This note was uploaded on 02/29/2008 for the course ME 242 taught by Professor Perreira during the Spring '08 term at Lehigh University .
- Spring '08