solution
by using linearity property of inverse laplace transform, we get
L-1{s+a/(s+a)2+b2}=e-at.cos(bt)
=e-3t(cos(3t)+2/3.sin(3t))
3. (4pts) Find L-1 S + 5 $2 + 6s + 18
Find 2-1 s +5 82 + 6s + 18 8.8 A BRIEF TABLE OF LAPLACE TRANSFORMS F(s) (s > 0) + (s > 0) (11 integer > 0) 1'(p+1) (P+1) (s >0) 1 094 (s >a) 8a n! (s = a)"+1 (* > 0) an integer >> 0) CONWt (3 > 0) sint (8 > 0) put coswt (8 - 1)? twa (* > 1) en sint (s > ) (8 - x)? Twº cosh (s > 100 sinh bt...
Find the inverse Laplace transformation of: a) F(s)- b) F,(s)--2 c) F(s) = 2,242 4 s2+6s +5 s2 +3s +1 3+2s+s s2 +9s +18 e) F(s)--一5 2s4 +12s+90 (s+2)(s +2s+2)
Determine L-'{F} F(s)= -252-6s+2 (s+2)(8+3) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-'{f}=0
find L^-1 {4s/s^2 + 2s -3} 4s Find L s2 + 25 - 3 5 -3t (write 5/6 by 6' , e^{-3t} bye and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
Determine Laplace transform of L{t sin3t}. O S $2 +9 O 6s (52 +9) None of them o S (52 +9) 2s (3² + 3)²
Find Inverse Laplace Transform 2s +1 (C) L-I{ s2 + 6s + 25
(4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1 (4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1
1. (3 points each) Find the following functions, (a) L{(t – 1) step(t – 4)} -4.5 (b) £'{S-2} } 2s + 1 (C) L-'{ s2 + 6s + 25
18. Consider the line L with vector equation (x, y, z)-(3, 4,-1 1,-2, 5) and the point P(2, 5, 7). Show that P is not on L, and then find a Cartesian equation for the plane that contains both P and L.