Tugas Matrek Laplace
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Nama : Khusnul Khotimah NRP : 24 11 100 703 Tugas : Matematika Rekayasa A. Selesaikan Transformasi Laplace Berikut. 1. L { 4 e 2t + 6 Sin 2t + 2t 6 } = L (4e 2t ) + L ( 6 Sin 2t) + L ( 2t 6 ) = 4L (e 2t ) + 6L (Sin 2t ) + 2L ( t 6 ) = 4 ( 1/s-2 ) + 6 ( 1/S 2 +2 2 ) + 4 (6!/6 6+1 ) = {4/(S-2)} + {6/(S 2 +4)} + {2880/ 6 7 } 2. L {e -5t Sin 5t}= L (e -5t ) L (Sin 5t) = (1/S+5) (5/S 2 +25) = {5/(S+5) 2 + 25} = {5/ S 2 +10S+50} 3. L (8 Cos 10t) = 8 L (Cos 10t) ={ 8 S/(S 2 + 10 2 ) } = {8S/(S 2 +100) } 4. L dari d 2 x/dt 2 + 12 dx/dt + 6x = Sin 3t, beserta fungsi transfernya.
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Transcript of Tugas Matrek Laplace
Nama : Khusnul Khotimah
NRP : 24 11 100 703
Tugas : Matematika Rekayasa
A. Selesaikan Transformasi Laplace Berikut.
1. L { 4 e2t + 6 Sin 2t + 2t6 } = L (4e2t ) + L ( 6 Sin 2t) + L ( 2t6 )
= 4L (e2t ) + 6L (Sin 2t ) + 2L ( t6)
= 4 ( 1/s-2 ) + 6 ( 1/S2+22) + 4 (6!/66+1) = {4/(S-2)} + {6/(S2+4)} + {2880/ 67}
2. L {e-5t Sin 5t}= L (e-5t) L (Sin 5t)
= (1/S+5) (5/S2+25)
= {5/(S+5)2 + 25}
= {5/ S2+10S+50}
3. L (8 Cos 10t) = 8 L (Cos 10t)
={ 8 S/(S2 + 102) }
= {8S/(S2+100) }
4. L dari d2 x/dt2 + 12 dx/dt + 6x = Sin 3t, beserta fungsi transfernya.
L (dx2/dt2) = s2 x (s) – sd2 x/dt2 (0) – dx/dt (0)
L (dx/dt) = 12x (s) – x (0)
L (x) = x (s)
L (y) = {3/(s2+9) }
f (s) adalah; xs (s2 + 12s +6) = {3/(s2 + 9) }Dapat dituliskan fungsi transfernya, (Output/Input) = 3/s4 +12s3 +15s2 +109s+54
B. Selesaikan Transformasi Laplace Balik Berikut.5. L-1 dari f (s) = {(s3 + 4s + 8)/ (s+2)2 }
Dengan perumusan yang telah ditentukan; b3 = (s+2)2 (s3 +4s+8)/(s+2)2 s = -2
= (-23 + 4. -2+ 8)
= 8
b2 = d/ds {(s+2) (s3+4s+8) /(s+2)2 } s = -2
= 2s2 + 4 s = -2
= 4
b3 = 1/2 d2/ds2 { s3+4s+8} s = -2
= 1/2 (4s) s = -2
= -4
f(s) = -4/(s+2)2 + 4/(s+2)2 + 8/(s+2)2
= 8/(s+2)2
f(t) = 8/s2+4s+4
= 2/s2+4s
= 2/s(s+4)
= 1/s(s+a)
=
