Math 2250-1Wed Nov 287.4 Forced oscillations for mass-spring systems. Application to models for earthquake-induced building vibrations.\302\267 Discuss forced oscillations for coupled mass-spring systems, with sinusoidal forcing: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 .Use yesterday's notes, starting on page 5. Our discussion will include "practical resonance" predictions.\302\267 Discuss how the same mathematics arises in the case of transverse oscillations. This discussion is also in yesterday's notes and is illstrated by a youtube video linked to there and here:http://www.youtube.com/watch?v=M_x2jOKAhZM Below is a discussion of how to model the "three-story" building shown shaking in the video above. This discussion relates to an earthquake project (modified from the one in the text for section 7.4), which is an optional project about a four story building that you may choose to complete. The project is posted on our homework page and if you try it you can use your score out of 20 points to replace your lowest homework or Maple project score from earlier in the course. You may use Maple, Matlab, Mathematica, Wolfram alpha - whatever software you prefer. You will upload your results to CANVAS.modeling the 3 story building, as in the youtube video:The ground is moving sinusoidally with amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ,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 acceleration 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 accelerations of the three massive floors (the top one is the roof) above ground and of mass LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, relative to the frame of the moving ground are therefore given 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 .Note the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv value in the last diagonal entry of the matrix. This is because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInRGJ0YyRjVGPkY+Rj4= is measuring displacements for the top floor (roof), which has nothing above it. Exercise 1) Derive the system of DE's above.Here is eigendata for the unscaled matrix 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 . For the scaled matrix you'd have the same eigenvectors, but the eigenvalues would all be multiplied by the scaling factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1GLzYlUSJtRidGMkY1RjJGNS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGQi8lKWJldmVsbGVkR1EmZmFsc2VGJy1GLzYjUSFGJy9GNlEnbm9ybWFsRic= and the natural frequencies would all be scaled by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbXNxcnRHRiQ2Iy1GIzYkLUkmbWZyYWNHRiQ2KC1GLDYlUSJrRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRiw2JVEibUYnRjxGP0Y8Rj8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkwvJSliZXZlbGxlZEdRJmZhbHNlRicvRkBRJ25vcm1hbEYnRlJGK0ZS. Symmetric matrices like ours (i.e matrix equals its transpose) are always diagonalizable with real eigenvalues and eigenvectors...and you can choose the eigenvectors to be mutually perpendicular. This is called the "Spectral Theorem for symmetric matrices" and is an important fact in many math and science applications...you can read about it here: http://en.wikipedia.org/wiki/Symmetric_matrix.) If we tell Maple that our matrix is symmetric it will not confuse us with unsimplified numbers and vectors that may look complex rather than real.QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJLkxpbmVhckFsZ2VicmFHRiUhIiI=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QzA+SSplaWdlbmRhdGFHNiItSS1FaWdlbnZlY3RvcnNHRiU2Iy1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkSSJBR0YlL0kmc2hhcGVHRiVJKnN5bW1ldHJpY0dGJSEiIj5JKGxhbWJkYXNHRiUmRiQ2IyIiIkYzPkkpZXZlY3RvcnNHRiUmRiQ2IyIiI0YzPkknb21lZ2FzR0YlLUkkbWFwR0YsNiRJJXNxcnRHRissJEY1RjNGOD5JImZHRiVmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJComLUkmZXZhbGZHRiw2I0kjUGlHRixGODkkRjNGPUYlRiVGJUYzPkkocGVyaW9kc0dGJS1GQTYkRkZGP0Y4PkktZWlnZW52ZWN0b3JzR0YlLUZBNiRGUEY6Rjg=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Exercise 2) Interpret the data above, in terms of the natural modes for the shaking building . In the youtube video the first mode to appear is the slow and dangerous "sloshing mode", where all three floors oscillate in phase, with amplitude ratios LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEjMzNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSI6RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYsNiRRIzU5RidGL0YyLUYsNiRRIzc0RidGL0Yv from the first to the third floor. What's the second mode that gets excited? The third mode? (They don't show the third mode in the video.)Exercise 3) Could you modify the matrix algebra, and then the commands in yesterday's notes, to create practical resonance graphs as we did there? Remark) All of the ideas we've discussed in section 7.4 also apply to molecular vibrations. The eigendata in these cases is related to the "spectrum" of light frequencies that correspond to the natural fundamental modes for molecular vibrations.TTdSMApJN1JUQUJMRV9TQVZFLzQ0MjM1NjU1NzZYLCUpYW55dGhpbmdHNiJGJVtnbCEiJSEhISMqIiQiJCQhIz8hIiIiIiIiIiFGKSEiI0YpRipGKUYoRiU=TTdSMApJN1JUQUJMRV9TQVZFLzQ0Mzg1NDc2NDBYKiUpYW55dGhpbmdHNiJGJVtnbCEjJSEhISIkIiQkIiY+IT0hIiUkIiZxQyJGKCQiJi9YJSEiJkYlTTdSMApJN1JUQUJMRV9TQVZFLzQ0Mzg1NDc3NjBYKiUpYW55dGhpbmdHNiJGJVtnbCEjJSEhISIkIiQkIiZxWyQhIiUkIiYnUV1GKCQiJj1UIiEiJEYlTTdSMApJN1JUQUJMRV9TQVZFLzQ0Mzg1NDc4ODBYLCUpYW55dGhpbmdHNiJGJVtnbCEiJSEhISMqIiQiJCQhJiwiZiEiJiQiJilwdEYoJCEmKnpLRigkISYpcHRGKEYrJCImLCJmRigkIiYqektGKEYvRilGJQ==