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Tugas Matematika Teknik Bu Inggrid
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TUGAS INDIVIDU
MATEMATIKA TEKNIK II
OLEH :
HARI MURTI FITRIANNO D41114703
UNIVERSITAS HASANUDDIN
FAKULTAS TEKNIK
JURUSAN TEKNIK ELEKTRO
2015
15. r(t) = ( ), < < ( + ) = ( )
P = 2L2 = 2L =Fungsi Ganjil Maka an = 0
a0 = ( ).a0 = ( ).= ( ).= += + = 0
bn = ( ). sin= ( ) . sin .
Rumus : (dv) = . ( )Integral 1:= ( )
-15
-10
-5
0
5
10
15
-4 -2 0 2 4
t(phi^2-t^2)
t(phi^2-t^2)
Intergral 1
= 3 , = ( 3 ).= sin= sin = . cos= ( ). . cos ( 3 ). . cos= ( ). . cos + ( 3 ). cos
Rumus : (dv) = . ( )Integral 2:= ( 3 )= 6 , = 6 .= cos= cos = . sin
= ( 3 ). . sin 6 . . sin= ( 3 ). . sin + 6 . sin
Rumus : (dv) = . ( )Integral 3:= 6= 6, = 6.= sin= sin = . cos
= 6 . . cos 6. . cos= . cos + . sin= . sin . cos
Intergral 2
Intergral 3
Jadi
bn = ( ). . cos + ( 3 ). . sin + ( 3)= ( ). . cos + ( 3 ). . sin + . ( . sin . cos )= ( ). . cos + ( 3 ). . sin + . sin . cos= ( ). . cos + ( 3 ). . sin + . sin . cos= ( . ). . cos + 0 + 0 . cos + ( . ). . cos + 0 + 0 +. . cos= 0 . cos + 0 . cos= . cos= .
b1 = 12
b2 = -3/2
b3 = 4/9
Jadi Fungsi r(t) = + +Gambar :
Fungsi Y(t)+ + = ( )= . cos + . sin= . sin + . n cos= . cos . sin+ + = 12 cos . cos . sin nt Knc. sin nt + Mnc. cos nt + K. cos nt + M. sin nt = 12 cos( +Mnc + K). cos nt + (M Knc + M). sin nt = 12 cos + 0. sin + Mnc + K = 12 Knc + M = 0( + 1). + . = 12 (1 ). K + nc.M = 12( ). + (1 ).M = 0
-15
-10
-5
0
5
10
15
-4 -3 -2 -1 0 1 2 3 4
12 sin t-3/2 sin 2t4/9 sin 3tTOTAL
= 123 1 21 2 1 2 = 123 .(1 2) = ( )= (1 ) + ( )= 1 2 12301 2 1 2 =
Jadi Fungsi y(t) :(12 12) . cos + 12 . sinBerikut Gambar untuk n=1,2,3 dengan c=1
-15
-10
-5
0
5
10
15
-4 -3 -2 -1 0 1 2 3 4
A1*cos tA2*cos2tA3*cos3tB1*sin tB2*sin2tB3*sin3tTOTAL