# ps10 - on mass m 1 Such components are use±ul in...

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2.14/2.140 Problem Set 10b (revised 5/4/07) Assigned: Thurs. May 3, 2007 Due: Thurs. May 10, 2007, in class Reading: F,P,E Sections 7.8,7.9.1 The following problems are assigned to both 2.14 and 2.140 students. Problem 1 Archive Problem 4.16 Problem 2 Archive Problem 4.18. For this problem, frst develop a state-space model with input F , and with two outputs x 1 and x 2 . Use the mass positions and velocities as state variables. That is, write your model in terms a state vector x = [ x 1 x ˙ 1 x 2 x ˙ 2 ] . Use this state-space model as the basis ±or calculating the trans±er ±unctions requested. Note that the ±ormula ±or the trans±er ±unction H ( s I F ) 1 G + J will give a trans±er ±unction matrix which contains the two desired trans±er ±unctions. You may use Matlab to calculate the trans±er ±unctions a±ter substituting in the numerical values given in part b); ±or this you can simply use the command ss2tf , and do not need to use the symbolic result above. That is, you do not need to give us a symbolic result ±or the trans±er ±unctions requested in part a); their numerical representation is suﬃcient. This mechanical structure can be used as a tuned mass absorber which, ±or a given sinusoidal disturbance F known ±requency, can reduce the amplitude vibration
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Unformatted text preview: on mass m 1 . Such components are use±ul in automotive, aerospace and other applications where vibrations might be a problem. Describe qualitatively how the ±orce on m 1 is “absorbed”. What design condition (relation between parameter values) would be required in order to have zero motion on m 1 ±or an input sinusoid in F o± known ±requency ω in ? Problem 3 Archive Problem 9.9. You solved the re±erenced Problem 9.4 on Problem Set 1. Please use your results or the solution results ±rom Problem 9.4 to answer part d) o± Problem 9.9. Problem 4 Archive Problem 13.1e–g Problem 5 Archive Problem 17.19 Problem 5 F,P,E Problem 7.52 Problem 6 F,P,E Problem 7.54 The following problems are assigned to only 2.140 students. Students in 2.14 are welcome to work these, but no extra credit will be given. Problem G1 F,P,E Problem 7.55 1...
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