Question

For transform #22 shown below, given S-03, A-1, and on-2, use Excel to graph ft) from t-0 to 8 seconds. Set up your graph to allow ζ to be a variable in a cell and use absolute addressing so that you quickly changethe value or and see the new step response. Show your final formula for f(t), including your calculation for W. Attach your graph to the end of the assignment. 8. system re sponse to step inpu where ψ-tan-1 (0<b<m)

Answer 1

Consider the function, F(s) A o7 F(s)= s(s2+2,s+ The inverse Laplace transform is, e A1 sin o A-12- 1-43 ;0 T V = tan 5<1 A 1 2 5 0.3 f(t) 11+ : sin 2, (A-1,2-1c) /1-5 V = tan 51 Use excel to graph f(t). Take as a variable. and sin 21-41-) vi-42 Calculate as two terms and then. calculate f(t) in Excel

Observe the formula for the two terms as shown AutoSave O Formulas File Home Insert Page Layout Data Review Sma Scre 3r Pivot Table Recommended Table Pictures Online Shapes lcons Pictures Models PivotTables Tables Illustrations -EXP( -2 " F2 " A2)/SQRT(1-F2^2) SUM X C E F G 1 1 Iterm Il term f(t) angle zeta olEXP(-2 F2 A2)/SQRT(1- F2^2 ) 2 0.5 -1.0472 3 0.2 0.5 -1.0472 -1.0472 4 U.. 1 -1.0472 AutoSave Off File Page Layout Formulas Review Home Insert Data Pictures Online Shapes 1cons D PivotTable Recommended Table Pivot Tables Models Pictures Tables Illustrations =sIN (2 SQRT ( 1- F2^2)*A2-G2) SU A C D 1 t f(t) angle I term - Il term zeta 1.154701 SIN(2*SQRT(1- F2^2) *A2-G2) 0.5 -1.0472 3 0.25 0.5 -1.0472 4 0.5 0.5 -1.0472 5 0.75 0 5 -1.0472 0.5 6 1 -1.0472 7 1.25 0.5 -1.0472 1.5 0.5 -1.0472 9 1.75 0.5 -1.0472 10 0.5 -1.0472 AutoSave O O File Formulas Review Home Insert Page Layout Data Sr PivotTable Recommended Table Pictures Online Shapes Icons Pictures 3D Models PivotTables Tables Illustrations -1+B2*C2 fe X SUM P A F G 1 t f(t) angle I term o 1.154701 0.8660251-1+ B2C2 Il term zeta 0.5 2 -1.0472 0.5 -1.0472 3 0.25 0.899282 0.9959 0.5 4 0.5 0.700361 0.941943 -1.0472 5 0.75 0,545442 0.714114 0.5 -1.0472 6 1 0.424791 0.354467 0.5 -1.0472

Copy paste the formula in Select all the columns for t ranging from 0 to 8. f(t columns. Go to Insert chart t and and select XY (scatter) type as shown Bock Excel utobaves Developer chart Deigne Fle Page Layous Farmulai Briew iew Hame Insert Data Hep Tarmat Sarch hSeatt Get Add-in mi Soeeashot Recanedel -.- Pivor Tble Recommended Table Pistures Ckre Shapes loons 6My Add Bn People Maes Graph Maps PivetChat Lise Coum Winh Lo Medel Pistures Oarts Map Tables utrere Adp-nm Chats Tours Sarkines Chart 3 Change Chart Tpe Reco mded Chat A Chert C E F G H A Recet Iterm Il bam pata angle Oc Tamplates ol 1.04325 0.35333 0.25 0502267 035197 1a11 05 0.7653 075 0.668436 0430079 1287472 10575313 0.0825 0.983e 1.25 0495175 -048762 0.758544 15 042620 083401 0.64546 175 0366334 -099423 0.6352832 20315737 0s3252 0.205568 225 0271758 -066265 0819519 25 0,233904 0.24487 0942724 275 0201323 0227572 1045816 017328 0649216 1112496 325 0.149144 0925942 1.138099 35 0128369 09688 1127853 375 0.110438 0843695 1093219 40093098 0503082 10478425 425 0.081352 45 0070451 -041394 0.970838 47 0.000537 -07806 50.052131-058199 0948749 52 0.0921 -05913 0.95915 55034-0.72217 0.972078 57 0.03327 -032401 098as217 a02543 0.346475 10041504 62 0.02553 o.s5426 101M0 65 002122 o.s1635 6 0.0182s4 0.199975 q.3 -1.2561 l Column 0.3 12661 Scatter with Smcot stewith Seeth Line 0654 16185834 -1.2661 Lne 03 -1.2661 6 -1.2661 7 0.3 -1.2661 MArea 8. 0.3 -1.2661 0.3 -1.2661 XYScatte 10 0.38 1 2661 Mep 11 0.38 -4.2661 Stecia 12 0.3 1.2661 Suface 13 03 4.2661 4.2661 Rader 14 0.3 15 0.3 1.2661 R Treemor 16 0.3 12561 Sunbur 17 0.3 -1.2661 Htegram 18 03 -1.2661 Bax& Whisker 0.00017 1004307 19 03 -1.2661 Wetefal 20 0.3 -1-2561 035236 21 0.3 -1-2663 Funnel 22 03 -1-2561 eCombo 23 0.3 1-2541 24 0.3 1.25 0.3 1.251 CAGet 26 0.3 -1.2551 2T q.a 1.2543 20 101852) q.3 -1.2551 29 1018263 0.3 -1.251 g.01572 0g5101 10135134 q.3 -1.251 7.23 q.3 75 0D11645 7. p010023 112382 10015425 q.3 .n 13744 n 715615 -1.2507 O00s27 -DT3154 0533- -1.2003

Obtain the plot for f(t) f(t) 2.5 15 1 0.5 8 2 3 5 7 Now change 5 value to 0.5 in the F-column and obtain the plot for f(t) f(t) 2.5 1.5 1 0.5 0 0 1 2 3 6 7