Question

4. Use the table of Laplace transforms and properties to obtain the Laplace transform of the following functions. Specify which transform pair or property is used and write in the simplest form. For part b, use the result of part pa (do not use # 28 in Table 2.2.1). For part c, use the result from part b. a. X(t) = sin 4t d. x(t) = e-St sin(4t) b. y(t) = t sin(4) e, y(t) = 1 + 3t2 c. z(t) = e-2[t sin(41)] f. z(t) = t4e-2

Answer 1

#Laplace Transform of As we know that 6 al = finft for FII = fin at IdFsly a . b (MA) = Lllingt) z 4 to 52 +42 ..83+16 a t hinata sem lbl y H= thingt By using the property LI FAY = Ligh dh fish in our case, n=1,

Lffesy = - 119 - ' ... Lekinetta - Lomach -- Les + 0 -4.25 (S2+142 / ... a thing the sc] ?14) ēt st fin 4+1 using the property LLEN H y = fismy. ww have, F111= thin 4+ 4 from B, f!= 85 (stroja - L { ēkt ffingtya 8 (5+2) | (s+2/²+16/2

(dl nuia est fintt Again from the propery we have nos heat PHI Yz fistas ao frs) = sample all insty lel JHI= +²+372 ALLYHY = 4 +3+3*?y z h&+34 + 3 h&t24 + 3 lucrare a meno di 5++ 54483 +34 + 12.4tdaging Ifi ruiz Atest ne +47 y z 4! ) du sew flv Y = fistas y