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20. For a tightly stretched string with 5 evenly spaced masses and Use MatLab to determine: a) the natural frequencies b) the mode shapes - plot them as in the example in the notes c) Show that the 1st and 3rd mode shapes are orthogonal with respect to the mass matrix d) Determine the responses for x₁, x, and x3 for 0} -1 mm and 1 0 01/mm/sec 0 e) Plot your results f) Show that system vibrates in the 4th mode shape if the initial displacements are the 4th mode shape Answer: [-.3626] [0]

20. For a tightly stretched string with 5 evenly spaced masses and Use MatLab to determine: a) the natural frequencies b) the mode shapes - plot them as in the example in the notes c) Show that the 1st and 3rd mode shapes are orthogonal with respect to the mass matrix d) Determine the responses for x₁, x, and x3 for 0} -1 mm and 1 0 01/mm/sec 0 e) Plot your results f) Show that system vibrates in the 4th mode shape if the initial displacements are the 4th mode shape Answer: [-.3626] [0]

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Matlab

20. For a tightly stretched string with 5 evenly spaced masses and Use MatLab to determine: a) the natural frequencies b) the mode shapes - plot them as in the example in the notes c) Show that the 1st and 3rd mode shapes are orthogonal with respect to the mass matrix d) Determine the responses for : 0-1 mm 1 -.3626 -.6280 d) {x(t)}=-.7251 .6280 .3626 and .4082 0 (0) e) Plot your results f) Show that system vibrates in the 4th mode shape if the initial displacements are the 4th mode shape Answer: x₁, x₂ and x, for 1 mm/ 0 0 nm/sec sin(.5176t+2.6639)+ f) All C₁=C₂ = C₂ = C₁=0 C₁=0 0 0 0 sin(t-1.0420)+ 0 0 4082 sin(1.4142t+2.1863) + 1 sin(1.7321t-1.5708)+ 0 .4082 .1877 -.3251 3753 sin(1.9319t-1.0931) .3251 .1877
Transcribed Image Text:20. For a tightly stretched string with 5 evenly spaced masses and Use MatLab to determine: a) the natural frequencies b) the mode shapes - plot them as in the example in the notes c) Show that the 1st and 3rd mode shapes are orthogonal with respect to the mass matrix d) Determine the responses for : 0-1 mm 1 -.3626 -.6280 d) {x(t)}=-.7251 .6280 .3626 and .4082 0 (0) e) Plot your results f) Show that system vibrates in the 4th mode shape if the initial displacements are the 4th mode shape Answer: x₁, x₂ and x, for 1 mm/ 0 0 nm/sec sin(.5176t+2.6639)+ f) All C₁=C₂ = C₂ = C₁=0 C₁=0 0 0 0 sin(t-1.0420)+ 0 0 4082 sin(1.4142t+2.1863) + 1 sin(1.7321t-1.5708)+ 0 .4082 .1877 -.3251 3753 sin(1.9319t-1.0931) .3251 .1877
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