lab 10 Modelownie liniowych układów dyskretnych2

restart:

with(LinearAlgebra):

with(plots):

#sortowanie proc

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#Zad1

E:=1/2*m*add(v[i]^2,i=1..5):

U:=1/2*k*add((x[i+1]-x[i])^2,i=1..4):

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#Zad2

n:=5:

K:=Matrix(n):

M:=Matrix(n):

for i to n do

for j to n do
K[i,j]:=diff(U,x[i],x[j]);
M[i,j]:=diff(E,v[i],v[j]);
end do;
end do;

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#Zad3

A:=1/M.K:

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#Zad4

m:=1: k:=100:

alpha,V:=evalf(Eigenvectors(A)):

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#Zad5

alpha,V:=sortowanie(alpha,V):

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#Zad6

for i from 1 to n do

w[i]:=V[1..n,i]/(sqrt((V[1..n,i]^%T).M.V[1..n,i])):
end do:

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#Zad7

for i from 1 to n do

omega[i]:=sqrt(alpha[i])
end do:

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#Zad8

x0:=Vector(5,[0,0,0,0,0]):

v0:=Vector(5,[10,0,0,0,0]):

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#Zad9

x:=(Transpose(w[1]).M.(x0+v0*t))*w[1]+add((Transpose(w[1]).M.(x0*cos(om
ega[i]*t)+v0*sin(omega[i]*t)/omega[i]))*w[i], i=2..5):