TI 85 Vibrations - Matrix Iteration Method Program

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Author: Michael Smetana

TI85, TI-85 Vibrations, Matrix Iteration Method Program for the TI 85 Calculator.  If you use the TI Graph Link Program just drag this to the board and send to your calculator. 

This solves for the upper and Lower Frequencies and mode shapes of 2, 3, 4, and 5 Degree of freedom systesm.

 Other wise, There will be two versions.  The first is the EXACT program, and the second is the Interpolated Program for others.

-------------EXACT TI85 - Matrix Iterations Program-------

:ClLCD
:Disp "ITERATION METHOD"
:Disp "FOR VIBRATIONS"
:Disp "DISTRIBUTED BY"
:Disp "WEATHAT.COM"
:Disp "........"
:Disp "PROGRAM YOUR MATRIES"
:Disp "A,AA=a,K,M"
:Pause
:ClLCD
:Disp "USE WHAT YOU KNOW TO"
:Disp "SOLVE FOR UPPER AND"
:Disp "LOWER FREQUENCIES AND"
:Disp "MODE SHAPES"
:Pause
:ClLCD
:Disp "Div by Zero Means"
:Disp "1 1 1 .. is your"
:Disp "mode shape"
:Disp "PICK WHAT MODE SHAPE"
:Disp "YOU WANT"
:Disp "UPPER OR LOWER"
:Disp "HAVE A MATRIX PUSH F5"
:Menu(1,"LOW",LL,2,"HI",HH,5,"A MATRIX",NN)
:Lbl LL
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:ClLCD
:Disp "DO YOU HAVE a OR K"
:Menu(1,"a",aa,2,"k",kk)
:Lbl aa
:ClLCD
:Disp "AA MATRIX IS a matrix"
:AA*MüA
:Goto LOOP
:Lbl kk
:Kñ*MüA
:Goto LOOP
:Lbl HH
:Menu(1,"a",YY,2,"k",ZZ)
:Lbl YY
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:Mñ*AAñüA
:Goto LOOP
:Lbl ZZ
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:Mñ*KüA
:Goto LOOP
:Lbl NN
:Prompt (N)
:Goto LOOP
:Lbl LOOP
:ClLCD
:Disp "HOW MANY DEGREES OF"
:Disp "FREEDOM"
:Menu(1,"2dof",TWO,2,"3dof",THREE,3,"4dof",FOUR,4,"5dof",FIVE)
:Lbl TWO
:[[1][1]]üX
:Goto MM
:Lbl THREE
:[[1][1][1]]üX
:Goto MM
:Lbl FOUR
:[[1][1][1][1]]üX
:Goto MM
:Lbl FIVE
:[[1][1][1][1][1]]üX
:Goto MM
:Lbl MM
:For(i,1,N)
:A*XüXX
:XX(1)üJ
:XX*(1/(norm J))üX
:ClLCD
:Disp "Â*(k/m)",J
:Disp X
:Pause
:End
:ClLCD
:Disp "WERE YOU SOLVING FOR"
:Disp "LOW OR HIGH NAT FREQ"
:Menu(1,"LOW",WW,2,"HIGH",VV)
:Lbl WW
:(ð(1/norm J))üR
:Goto EEE
:Lbl VV
:ð(norm J)üR
:Goto EEE
:Lbl EEE
:Disp "OMEGA",R

------------Interpolated - TI85 Program-----------

-> = sto

^(-1) is the inverse function ^-1

This Program if Edited for your Calculator will work for all TI calculators.  The menus are different for the TI83 and TI84, and so is the For Loop. I do not know how to edit it.  The TI89 should be close the the same format as the TI 83.  I will see If I can get these programs, as they have already been created and duplicated on my friends  TI83 calc.  Or If your nice enough Please post the code as a comment.

---------------------

:ClLCD
:Disp "ITERATION METHOD"
:Disp "FOR VIBRATIONS"
:Disp "DISTRIBUTED BY"
:Disp "WEATHAT.COM"
:Disp "........"
:Disp "PROGRAM YOUR MATRIES"
:Disp "A,AA=a,K,M"
:Pause
:ClLCD
:Disp "USE WHAT YOU KNOW TO"
:Disp "SOLVE FOR UPPER AND"
:Disp "LOWER FREQUENCIES AND"
:Disp "MODE SHAPES"
:Pause
:ClLCD
:Disp "Div by Zero Means"
:Disp "1 1 1 .. is your"
:Disp "mode shape"
:Disp "PICK WHAT MODE SHAPE"
:Disp "YOU WANT"
:Disp "UPPER OR LOWER"
:Disp "HAVE A MATRIX PUSH F5"
:Menu(1,"LOW",LL,2,"HI",HH,5,"A MATRIX",NN)
:Lbl LL
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:ClLCD
:Disp "DO YOU HAVE a OR K"
:Menu(1,"a",aa,2,"k",kk)
:Lbl aa
:ClLCD
:Disp "AA MATRIX IS a matrix"
:AA*M->A
:Goto LOOP
:Lbl kk
:(K^(-1))*M->A
:Goto LOOP
:Lbl HH
:Menu(1,"a",YY,2,"k",ZZ)
:Lbl YY
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:(M^(-1))*(AA^(-1))->A
:Goto LOOP
:Lbl ZZ
:ClLCD
:Disp "HOW MANY ITERATIONS"
:Prompt (N)
:(M^(-1))*K->A
:Goto LOOP
:Lbl NN
:Prompt (N)
:Goto LOOP
:Lbl LOOP
:ClLCD
:Disp "HOW MANY DEGREES OF"
:Disp "FREEDOM"
:Menu(1,"2dof",TWO,2,"3dof",THREE,3,"4dof",FOUR,4,"5dof",FIVE)
:Lbl TWO
:[[1][1]]->X
:Goto MM
:Lbl THREE
:[[1][1][1]]->X
:Goto MM
:Lbl FOUR
:[[1][1][1][1]]->X
:Goto MM
:Lbl FIVE
:[[1][1][1][1][1]]->X
:Goto MM
:Lbl MM
:For(i,1,N)
:A*X->XX
:XX(1)->J
:XX*(1/(norm J))->X
:ClLCD
:Disp "Â*(k/m)",J
:Disp X
:Pause
:End
:ClLCD
:Disp "WERE YOU SOLVING FOR"
:Disp "LOW OR HIGH NAT FREQ"
:Menu(1,"LOW",WW,2,"HIGH",VV)
:Lbl WW
:((1/norm J)^(1/2))->R
:Goto EEE
:Lbl VV
:((norm J)^(1/2))->R
:Goto EEE
:Lbl EEE
:Disp "OMEGA",R