eprintid: 8512
rev_number: 31
eprint_status: archive
userid: 71
dir: disk0/00/00/85/12
datestamp: 2013-07-03 09:03:10
lastmod: 2016-01-14 04:24:52
status_changed: 2013-07-03 09:03:10
type: thesis
metadata_visibility: show
creators_name: SYAMSUL ARIFIN, NIM.  07610002
title: METODE TRANSFORMASI LAPLACE MATRIKS 
DAN PENERAPANNYA PADA SISTEM PEGAS MASSA 

ispublished: pub
subjects: Matematika
divisions: jur_mat
full_text_status: restricted
abstract: There are several methods to solve an initial value problem of second-order 
homogenous linear systems of differential equations with constant coefficients.
That are elimination met hod and matrix method. Whereas to solve
nonhomogenous systems, used undetermined coefficient method and variation of
parameter method, that through some difficulties and complex procceses. But
then, there is an alternative method to solve it. It is Matrix Laplace Transform
Method. 

      The goals of the research are to explain Matrix Laplace Transform Method
and use it to solve init ial value problems of second-order  homogenous linear
systems of differential equations with constant coefficients that form  
    

(

)
= 
(

)

(

)
+ 
(

)
                    
(
1
)

where 

(

)
 is second derivative from 
(

)
. 
(

)
 is column vector from 
(),


(),…,
(). 
(

)
 is  ×  matrices form. All of matrix entries are constant. If
all entries of 
(

)
 equal zero, then
(
1
)
 said homogenous. If not, it is called
nonhomogenous. Hence, if value of 
(

)
 and '
(

)
 as initial conditions are 

known, or 
(


)
= 

 and '
(

, then (1) is an init ial value problem of
second-order linear systems. 

)
= '


      The result of the  research is be obtained solutions of second-order linear
systems of differential equations with constant coefficients use Matrix Laplace
Transform Method is 
 = L



 = L


(


 - 
)

xviii 



(

)
+ 
(

)
+ '
(

)

.
Then, appliying this met hod to solve initial value problems on spring-mass 
systems. That are undamped free motion of spring-mass systems, f ree motion with
damped and forced motion of spring-mass systems. 


Keyword : Matrix Laplace Transform Method, initial value problems, secondorder

systems of linear different ial equations with constant coefficients, springmass
systems.
date: 2013-05-08
date_type: published
institution: UIN SUNAN KALIJAGA
department: FAKULTAS SAINS DAN TEKNOLOGI
thesis_type: skripsi
thesis_name: other
citation:   SYAMSUL ARIFIN, NIM. 07610002  (2013) METODE TRANSFORMASI LAPLACE MATRIKS DAN PENERAPANNYA PADA SISTEM PEGAS MASSA.  Skripsi thesis, UIN SUNAN KALIJAGA.   
document_url: https://digilib.uin-suka.ac.id/id/eprint/8512/2/BAB%20I%2C%20V%2C%20DAFTAR%20PUSTAKA.pdf
document_url: https://digilib.uin-suka.ac.id/id/eprint/8512/1/BAB%20II%2C%20III%2C%20IV.pdf