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Exercise 10 matte 4 NTNU, mandatory exercise
Typology: Exercises
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Rule 4 states that:
Yt Estat Apply (^) Inearity Llfett
tet s
tet (^) at w^2 s
Rule 11 states that: First, apply linearity. Then we recognize the possibility to apply rule 4. EI Ietf så (^2) s O (^52) s
å 2 5
Isp GIVEN (^) s 2
Lleatcoslatl s^ a s a we SIMPLY (^) APPLY (^) RULE
sta 25
LCI (^) LCI Rute (^48) LCE TI I (^) J D^ VI^ HAR^ Altså^ t EN^ KONSEKVENS^ AV^
YE LI It L DV^ HAR^ ALTSÅ^ t EN^ KONSEKVENS^ AV^ DETTE^ ER^11 x 4 (^2) I Ut
We will do a partial fraction decomposition. Apply linearity For Blue we will apply rule 7. Rule 7 states that: For Red we will further linearize For green we apply rule 14. Rule 14 states that For orange we apply rule 13. Rule 13 states that s (^) jeg s DIT
As (^) A BJ S^ BS^ C I At B O^ A^ C^1
I C^133 0 26 2 0 I^ i
Fas sh^ stil EFN Bass^ RIS Leat Fa Boss (^) et
til List^ cos at^ s wa GU cos^ t utsin^ ut stor 201s sin^
2 Fis^ et^ cos^ t^ sin^
True, this follows from the Laplace transforms linear properties. By linearity we mean that for all numbers a, b: L(af + bg) = aL(f) + bL(g).
g test L f^ g LIF^ g^ I^ Fa
Def av^ Laplace^ f^ festfetsdt
Ø
Ny seks^ sycos^ glo^
fly sYass^ glo 5 d (^) y Yes^6 5Yss (^) sycos y'los^5 syd^ geol 6 Yes^ 0 5 Yess^ SC^2 1 5 sYes (^) C^2 GYess^0
0 S (^) i 2s^9 se se^ III Is (^2) Is 3
Sts B S^2
II II A 2 Bylt (^322 5) e
i (^9) B 3 B e^3 A (^5)
