Title | Jawaban contoh soal Transformasi Laplace |
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Author | Ester Herlina |
Pages | 3 |
File Size | 27.5 KB |
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Jawaban contoh soal Transformasi Laplace 1. Hitung: L [10 sin 4t + 4t 2] Jawab: L [10 sin 4t + 4t 2] = L[10 sin 4t ] L[4t 2 ] = 10L[sin 4t ] 4L[t 2 ] 4 (3) = 10. 2 4. 3 s 4 2 s 40 4.2! = 2 3 s 16 s 40 8 = 2 3 s 16 s 2. Hitung : L[e 5t (sin 2t sin 4t )] Jawab : L[e 5t (sin 2t sinh...
Jawaban contoh soal Transformasi Laplace
1. Hitung: L [10 sin 4t + 4t 2] Jawab: L [10 sin 4t + 4t 2] = L[10 sin 4t ] L[4t 2 ] = 10L[sin 4t ] 4L[t 2 ] 4 (3) = 10. 2 4. 3 2 s 4 s 40 4.2! = 2 3 s 16 s 40 8 = 2 3 s 16 s 2. Hitung : L[e 5t (sin 2t sin 4t )] Jawab : L[e 5t (sin 2t sinh 4t )] L[e 5t sin 2t ] L[e 5t sinh 4t ].......(1) L[sin 2t ]
2 s 4 2
L[e 5t sin 2t ]
2 ( s 5) 2 4 2 = 2 s 10s 25 4 2 ……………….(2) = 2 s 10s 29 4 L[sinh 4t ] 2 s 16 4 L[e 5t sinh 4t ] ( s 5) 2 16 4 = 2 s 10s 25 16 4 ………………(3) = 2 s 10s 9 Sehingga persamaan (2) dan (3) disubstitusikan pada persamaan (1), sehingga 2 4 L[e 5t (sin 2t sin 4t )] = 2 - 2 s 10s 29 s 10s 9
5,0, t 3 3. Hitung : L[ F (t )] , jika F(t) = 0, t 3 Jawab:
L[ F (t )] e st F (t )dt
= e st .5.dt e st .0.dt 0
3
= e st .5.dt 0
3
3
= 5 e st dt 0
3
0
5 = e st ]30 s 5 = (1 e 3s ) s
cos(t 2 / 3), t 2 / 3 4. Hitung : L[ F (t )] , jika : F (t ) 0, t 2 / 3 L[F(t)] = e st F (t )dt
0
e
2 / 3
=
e
st
0
=
.0.dt
e
st
cos(t 2 / 3)dt
2 /3
st
cos(t 2 / 3)dt
Subs. u (t 2 / 3) , du = dt Batas integrasi, t u t 2 / 3 u 0 2 /3
L[F(t)] e s (u 2 / 3) cos udu
0
= e
2 / 3
e
0
st
cos udu
= e 2 / 3 L[cos u] s = e 2 / 3 . 2 s 1 2 / 3 se = 2 s 1
t 5. Hitung : L[( ) 2 ] ! 4 Jawab: (3) L[t 2 ] 3 s 2! = 3 s 2 = 3 s 1 2 2 L[( ) ] = 4 . s 3 4 ( ) 1/ 4 8 = 3 3 4 .s 1 = 3 8s...