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190383355-Contoh-Soal-dan-jawaban-Transformasi-Laplace.pdf
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190383355-Contoh-Soal-dan-jawaban-Transformasi-Laplace.pdf
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AserWilli
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Jawaban contoh soal Transformasi Laplace
1. Hitung: L [10 sin 4t + 4t 2] Jawab: 2 L [10 sin 4t + 4t ] = L[10 sin sin 4t ] L[4t 2 ] = 10 L[sin 4t ] 4 L[t 2 ] (3) 4 4 . = 10. 2 2 3 s 4 s 40 4.2! 3 = 2 s 16 s 40 8 = 2 3 s 16 s
2. Hitung : L[e5t (sin 2t sin 4t )] Jawab : 5t 5t 5t L[e (sin 2t sinh 4t )] L[e sin 2t ] L[e sinh 4t ].......(1) L[sin 2t ]
L[e
5t
2 s
sin 2t ]
= = L[sinh 4t ] L[e
5t
4
2
2 ( s 5) 2 4 2 s
2
s
2
10s 25 4 2
10s 29
……………….(2)
4 s
2
sinh 4t ]
= =
16 4 ( s 5) 2 16 4 s
2
s
2
10s 25 16 4
10s 9
………………(3)
Sehingga persamaan (2) dan (3) disubstitusikan pada persamaan (1), sehingga 2 4 5t - 2 L[e (sin 2t sin 4t )] = 2 s 10s 29 s 10s 9
3. Hitung :
L[ F (t )] ,
5,0, t 3 jika F(t) = 0, t 3
Jawab:
e
L[ F (t )]
st
F (t )dt
0
3
e
=
st
.5.dt
0
e
st
.0.dt
3
3
e
=
st
.5.dt
0 3
=5
e
st
dt
0
= 5
=
4. Hitung :
s
5
e
st 3
]0
s
(1 e 3 s )
L[ F (t )] ,
jika :
F (t )
cos(t 2 / 3), t 2 / 3 0, t 2 / 3
e
L[F(t)] =
st
F (t )dt
0
2 / 3
e
=
st
.0.dt
0
e
st
cos(t 2 / 3)dt
2 / 3
e
=
st
cos(t 2 / 3)dt
2 / 3
Subs. u (t 2 / 3) , du = dt Batas integrasi, t u t 2 / 3 u 0
L[F(t)]
e
s ( u 2 / 3)
cos udu
0
=
e
2 / 3
e
st
cos udu
0
=
e
=
e
=
2 / 3
L[cos u]
2 / 3
se s
.
s s
2 / 3
2
1
2
1
t
5. Hitung : L[( ) 2 ] ! 4 Jawab: (3) 2 L[t ] 3 s
=
2! s
=
2 s
L[(
1 4
3
3
2
)2 ] = 4 .
( = =
s
1/ 4
8 3
4 . s 3 1 8 s 3
)3
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