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Natural Frequencies and Mode shape vectors for 10 Mass-Spring system

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Natural Frequencies and Mode shape vectors for 10 Mass-Spring system

  1. 1. Page 1 of 2 Natural Frequencies and Mode Shapes To obtain the natural frequencies and mode shapes the following program was setup in a m-script file: Natural Frequencies obtained:
  2. 2. Page 2 of 2 Block 1 0.1230 Block 2 0.2434 Block 3 0.3590 Block 4 0.4672 Block 5 0.5659 Block 6 0.6530 Block 7 0.7269 Block 8 0.7860 Block 9 0.8291 Block 10 0.8553 As obtained in program: With variable name nat_freq, all the natural frequencies of the 10 blocks are stored it in matrix form. It is obtained in the program as follows: nat_freq = Columns 1 through 9 0.1230 0.2434 0.3590 0.4672 0.5659 0.6530 0.7269 0.7860 0.8291 Column 10 0.8553 Mode Shapes: For Vector 1: 0.0439 0.0842 0.1177 0.1416 0.1541 0.1541 0.1416 0.1177 0.0842 0.0439 For Vector 2: -0.0842 -0.1416 -0.1541 -0.1177 -0.0439 0.0439 0.1177 0.1541 0.1416 0.0842 For Vector 3: -0.1177 -0.1541 -0.0842 0.0439 0.1416 0.1416 0.0439 -0.0842 -0.1541 -0.1177 For Vector 4: 0.1416 0.1177 -0.0439 -0.1541 -0.0842 0.0842 0.1541 0.0439 -0.1177 -0.1416 For Vector 5: -0.1541 -0.0439 0.1416 0.0842 -0.1177 -0.1177 0.0842 0.1416 -0.0439 -0.1541 For Vector 6: 0.1541 -0.0439 -0.1416 0.0842 0.1177 -0.1177 -0.0842 0.1416 0.0439 -0.1541 For Vector 7: 0.1416 -0.1177 -0.0439 0.1541 -0.0842 -0.0842 0.1541 -0.0439 -0.1177 0.1416 For Vector 8: 0.1177 -0.1541 0.0842 0.0439 -0.1416 0.1416 -0.0439 -0.0842 0.1541 -0.1177 For Vector 9: -0.0842 0.1416 -0.1541 0.1177 -0.0439 -0.0439 0.1177 -0.1541 0.1416 -0.0842 For Vector 10: -0.0842 0.1416 -0.1541 0.1177 -0.0439 -0.0439 0.1177 -0.1541 0.1416 -0.0842

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