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# me445_hw5 - to solve the equation 2000 4 t F x x =&&...

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ME 445 Mechanical Vibrations // Fall 2009 Homework #5 Due: 14.12.2009 1. A spring-mass system shown below has a Coulomb damper, which exerts a constant friction force f. For a base excitation, show that the solution is ( ) n 1 n n 0 n 1 0 z f.t 1 1 1 cos t sin t v t mv ω = - - ω - ω ω where the base velocity shown is assumed. k m f t 1 v 0 2. For t>t 1 show that the maximum response of the ramp function shown below is equal to ( ) n 1 0 n 1 max xk 1 1 2 1 cos t F t = + - ω ω Obtain a plot of the maximum response as a function of t 1 / τ . 3. An undamped spring-mass system is given a base excitation of ) 5 1 ( 20 ) ( t t y - = . If the natural frequency for the system is ω n =10 rad/s, determine the maximum relative displacement. 4. Determine the time response for Problem 3 using numerical integration. 5. This problem uses the program runga.m ( ftp://ftp.prenhall.com/pub/esm/mechanical_engineering.s-048/thomson/theory_of_vibration/runga.m
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Unformatted text preview: ) to solve the equation ) ( 2000 4 t F x x = + & & with initial conditions 1 1 = = x x & , for three different forcing functions. These forcing functions can be found below. Too see how these forcing functions differ, plot each one of them. Produce a plot of the response and discuss how the response differs as the forcing function is changed. (a) The MATLAB code is force1.m ( ftp://ftp.prenhall.com/pub/esm/mechanical_engineering.s-048/thomson/theory_of_vibration/force1.m ). (b) The MATLAB code is force2.m ( ftp://ftp.prenhall.com/pub/esm/mechanical_engineering.s-048/thomson/theory_of_vibration/force2.m ). (c) The MATLAB code is force3.m ( ftp://ftp.prenhall.com/pub/esm/mechanical_engineering.s-048/thomson/theory_of_vibration/force3.m ). t F(t) t 1 F M M...
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