EJERCICIOS DE TRANSFORMADA DE LAPLACE
1. L (et
+ senh2t) = L (et
) + L (sen h2t)
L (et
)= 1/s-1
L (senh2t)= 2/s2
-22
L (et
+ se h 2t)= 1/s-1+ 2/s222
= 1/(s-1) + 2/ (s+2) (s-2)
= (s+2) (s-2) + 2 (s-1)/ (s-1) (s+2) (s-2)
= s2
- 22
+2 s -6/ (s-1) (s+2) (s-2)
=...
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EJERCICIOS DE TRANSFORMADA DE LAPLACE
1. L (et
+ senh2t) = L (et
) + L (sen h2t)
L (et
)= 1/s-1
L (senh2t)= 2/s2
-22
L (et
+ se h 2t)= 1/s-1+ 2/s222
= 1/(s-1) + 2/ (s+2) (s-2)
= (s+2) (s-2) + 2 (s-1)/ (s-1) (s+2) (s-2)
= s2
- 22
+2 s -6/ (s-1) (s+2) (s-2)
= 12
+ 2 (1)-6/ (1-1) (1+2) (1-2)
= -3/0
= - ∞
2. L (2T-1)3 =
L 8t3
+12t2
+ 6t - 1
L 8t3
+ L 12T2
+ L 6T L 1
= 8*31
/S3+1
+ 12*21
/5 2+1
+ 6*1/S2
-1/S
= 48/S4
+ 24/S3
+ 6/S2
-1/S
= 48/14
+ 24/13
+ 6/12
-1/1= 86
= 48+24+6-1= 77
3. L (cos2t+1/2) = ½ (L(cos2t)+ L(1))
= ½ (B/S2
S2
) + 1/5
= ½ (1/12
+22
) + 1/1
= ½ (1/5 + 1)
= ½ (6/5)= 3/5
4. L (et
cos t + 4 et
sen t) = L (et
cos t) + L (4 et
sen t)
= L (et
cos t)= s-1/ (s-1)2
+ 1 2
= L (et
cost + 4 et
sen t )
= s-1/(s-1)+12
+ 4* 1/(s-1)2
+ 1
= s-1+4/(s-1)2
+1 = 1+3/(1-1)2
+1= 4/0+1
= 4/1
= 4
L. (4T3
*e-3t
)
= 4*31
/ (5+3) 4
= 24/(s+3)4
= 24/ (4)4
= 24/256 = 12/128 = 6/24
= 3/32= 1/32
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