hệ thống lí thuyết và bài tập chuyên đề dao động cơ học - Pdf 24

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  !
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−./012/345∋678/9/:









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=>/2/346
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&Ξ/(#∋/(∋ρ}∗ΨΖ∗+∗(/ΚΤς∃#Τς∗+Τ(µ#,∀∗Ψ∋Ο.
∃%&∋&,−
ζ∀)ΨΖ∗+Ψ#∋(∀∃Ξκ∀)ΨΖ∗+Τς)∗+Ψ∃#ΨΖ/π∀&ΣΤ∃Ξ!ΖΤ(Ξ!/#∗Κ()/#∗Ο/π∀Τ(ο#
+#∀∗.
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&#.
  2_Κ!/!()/ς∀κΟ%Ξ,#σ∗ΨΖΚ∃#ΨΖ//Ψ#/π∀&ΣΤΟ/(),#ΤΨΖ∃ϖ/(//Ψ#/π∀
&ΣΤ)&#.
 ΚΤζΟΚς∀κΟ%Ξ(∀/π∀κ∀)ΨΖ∗+Τ#Τ(ο#Ψ#}!Τ/(),#ΤΤς∗+Τ(µ#κ∀)ΨΖ∗+Κ&ν
Τς&Ξ/(#∋/(∋ρ}∗ΨΖ∗+Ο/π∀
  &ΣΤΤ(ο#Ψ#}!Τ.
  Κς∀κΟ%Ξ(∀,∀∗Ψ∋/π∀κ∀)ΨΖ∗+/(),#ΤΤς∗+Τ(µ#,∀∗Ψ∋/π∀&ΣΤ.
  Κς∀κΟ%ΞΤ∗Υ+//π∀κ∀)ΨΖ∗+Ψ#∋()Ξ/(),#ΤΤΥ/ΨΖ,#∗Τ(#σ∗+/(∀
ζ#}!6κ∀)ΨΖ∗+Ψ#∋(∀Τςσ∗!ΖΤΨ)∗Τ(∗+∃∋∗∃∋∗/Τ(}κξ//)#∃Ξ(Ω∗(/(#∋/π∀
!ΖΤΨ#}!Α/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋Τςσ∗Ψο∗+∗(∃ΞΨ)∗Τ(∗+Ψ.
∃./0∀∗123)&∋&,+
ζ(∋ΩΚΟ%Ξ()∗+Τ(ο#+#∀∗Ψ}Τ(/(#ϖ∗!ΖΤκ∀)ΨΖ∗+Τ)Ξ∗(∗.
 (∗(∃Ξ()∗+Τ(ο#+#∀∗∗+υ∗∗(ΤΨ}&ΣΤΤς∃#&νΤς&Ξ/(#∋/(∋ρ}∗ΨΖ∗+∗(/ΚΤς

ζ#∀ΤΥ/∃ΞΨ)(Ξ!,Σ/∗(Τ/π∀&Σ∗ΤΥ/ΚΨ)(Ξ!,Σ//π∀∃#ΨΖΟΤ()Τ(ο#+#∀∗%∀&
Ν€€

2/)ΚΤζΟ

Ν
?≅9/0≅/≅6




Ε

#∀ΤΥ//π∀&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀,#∗Τ(#σ∗Ψ#∋(∀/∗+Τ∗Υ∗(∗+∗+ξ/(∀&#∃#
ΨΖΚ!(∀


)&#&Σ∗ΤΥ/Ο.
 ϒ/Τ|+#∀ΤΥ//π∀&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀∃∋∗(∗+&&νΤς/∗,∗+&ΞΤ′∃ϖ&#ΨΖ∃∗
/π∀∃#ΨΖ.
 τ&νΤς,#σ∗ΚΝ2ΟΜ+#∀ΤΥ//ΨΖ∃∗//Ψ#%∀
!∀Ν


2.
 #µΤςνΨ#Υ%∀
!∀Ν


2(#Ν2∀

Ε#∀ΤΥ/Τ♣/Τ(ο#%∀


2/)Κ

Τζ

Ο


Ν



∃∋∗(∗+&&νΤς/∗,∗+
ΦΣΤ%Ν_&
Α∀Ν


2∀
Α#∗
_
ΣΤ,#σ∗%Ν♦2&
Α#∗
_∀
Α∀Ν



2

    
    


     
 
 Κ Ο   Κ Ο
 

       
     
    

!∀)ΨΖ∗+Ψ#∋()Ξ/Τ∗Υ+/∃Ξ

ΜΤ∗ΥΜ/(∋∞.(ΩΨΖ∗+∗♥∗+&ΞΤ(∗♥∗+,#∗
Τ(#σ∗&#Τ∗Υ+/

ΜΤ∗ΥΜ/(∋∞
Ζ∗+∗♥∗+&ΞΤ(∗♥∗+Τς∋∗+,Ω∗(Τς)∗+Τ(ο#+#∀∗∗Κ∗
η
Μ
∃Ξ/(∋∞κ∀)ΨΖ∗+Ο∃Ξ%
 
 
 8
 











&ΞΚ
 
_ Μ
  
 
Ο
(#∋κΞ#∼∋≤Ψ)%2
Η∋↔∗+Ψο∗+Ψ#Τς)∗+/(∋∞∃∋∗∃Ξ82Τς)∗+/(∋∞
∃∋∗∃Ξ2
2
2
ΝΝ
Α
Α
Α
Α
3








Τ

∗ζ

ΤΚ∗←_↑

ΤΟ
Η∋↔∗+Ψο∗+Ψ#Ψξ/Τς)∗+Τ(ο#+#∀∗∗∃ΞΛ

8∗2ΜΤς)∗+Τ(ο#+#∀∗

Τ∃ΞΛ

.
Η∋↔∗+Ψο∗+Τω∗+/Ζ∗+∃ΞΛΛ

ζΛ

:;<ζ∋

ΤΤ(ΩΛ

2
ζ∗(Λ

,∗+/µ/(Ψν∗(&νΤςΝ

ΜΝ





Η∋↔∗+Ψο∗+∃∗∗(Τ(#&ΣΤΨ#Τ♠Α

Ψ∗Α

ΨΥ#Ν♣∗+∼∋∀Τς⁄/#∗Κ(Ω∗(Ο

∀Ν
2 #∗







Η∋↔∗+Ψο∗+∗(°∗(Τ(#&ΣΤΨ#Τ♠Α

Ψ∗Α

ΨΥ#Ν♣∗+∼∋∀Τς⁄//)Κ(Ω∗(Ο
 Κ ) Ο


  


 

Τ%

∀Ν
∀Ν







&Ξ







&#Λ
Α∀Ν
Λ
Α#∗
Τ∗(∗(Τςσ∗.
Εµ/,/∃Σ(|∗+ΤςΩ∗(κ∀)ΨΖ∗+κ∀)ΨΖ∗+Ψ#∋()Ξ%
 η∗(


 η∗(2
 η∗(






3

6

Ν

Ν

3





Α

Α

2

2

6



Ψ
Μ×Ο∃∗
Τ(♣∗
 η##(|∗+ΤςΩ∗(∃ξ∗++#µ/∃ρ/µ/∗+(#ϖ!/π∀ΤΚ#Τ_Τ(∋Ζ/(!&#+#µΤςν
/π∀Ο
 η#ϖΤσ∗∗+(#ϖ!Ψ∋Τ#σ∗ΚΤ(ο∗+∗∗(°Ο
 η(ο#Ψ#}!Τ(♣∗/(∗(∃Ξ+#µΤςν∃∗Τ(♣∗
∋∗ΙϑΗς∀Τ(ο∗+/()+#µΤςν∗∗(°Μ/∗∗∋∗∃∗Τ(ΩΤΩ!∼∋ρ∃∋ΣΤΨ}∋ρς∀∗+(#ϖ!Τ(♣
∗
ζ  Τ(} +## ,Ξ# Τ)µ∗ ,∗+ /µ/( → κ⁄∗+ !Υ# ∃#σ∗ (ϖ +#∀ κ∀) ΨΖ∗+ Ψ#∋ ()Ξ &Ξ
/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋
Γµ/,/+##,Ξ#Τ)µ∗ΤΩ!Υ∃∗&ΣΤΨ#∼∋∀&νΤςΨ↔,#ΤΝΚ()/&Μ∀Μ
Τ
Μ
Ψ
Μ×ΟΤ♠Τ(ο#
Ψ#}!Τ

Ψ∗Τ

.
 η##(|∗+ΤςΩ∗(∃ξ∗++#µ/Ψξ//µ/∗+(#ϖ!
 η♠Τ

Τ↑Τ

Τ(∋Ζ/6(!&#+#µΤςν/π∀Κ#←∝Ο
 ηω∗+Υ+#µΤςν/π∀/(∗(∃ΞΥ∃∗&ΣΤΨ#∼∋∀&νΤςΨ.
:;<ζΤ(}+##,Ξ#Τ)µ∗,∗+/µ/(→κ⁄∗+!Υ#∃#σ∗(ϖ+#∀κ∀)ΨΖ∗+Ψ#∋()Ξ&Ξ
/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋.

   


    

()/
Ν 2/)Κ Ο
2#∗Κ Ο

 
 
  
   


    



!.∀)ΨΖ∗+/(|∗+ΤςΩ∗(Ψ/,#ϖΤ%
 ηΝ∀

2/)Κ

Τζ

Ο&#∀/)∗Τ
 #σ∗ΨΖ∃Ξ2ΜΤ∗Υ+/∃Ξ

Μ(∀,∀∗Ψ∋←

2/)

Κ

Τζ

ΟΚΤ∀(,Σ/Ο
 #σ∗ΨΖ2Τ∗Υ+/

Μ(∀,∀∗Ψ∋










=



=>//=Κ9−/Λ=0ΜΝ=

99/0≅/≅6Ο

Κψ3ΦΜΧΦΓΦϑ;<6>3≠Ο
Π5Θ5#5Ρ5Σ5

  
()/

. .#∗Κ . Ο
  
  
  
&Ξ
.

  
 
.
ζ∋Ψ↔Νµ/Ψν∗(Ψξ/∃#ΨΖΝΜΤ∀/Τ(}Νµ/Ψν∗(+#∀ΤΥ/Μ∃/(⁄/(θ#Τ(),#}∋Τ(♣/∗(
∀∋%

.
 

 
&Ξ

. . .

    

   

ζ(±≡%(#
_ _

  


  
Κ/!Ο.
/Ο
Ε. )Κ . Ο
  

 
Κ/!Ο.κΟ
_.#∗ΚΕ. . Ο

 


 
Κ/!Ο.
∆.6(|∗+ΤςΩ∗(κ∀)ΨΖ∗+/π∀!ΖΤ&ΣΤ∃Ξ%ΝΡ/)Κ8Τζ
Ρ

ΟΚ/!ΟΜ&#ΝΤ∗(,∗+/!ΜΤΤ∗(
,∗+.Χµ/Ψν∗(∃#ΨΖΜ&Σ∗ΤΥ/&Ξ+#∀ΤΥ//π∀&ΣΤ(#Τ_ΜΕ.


∀Ο
Ε. )Κ8. . Ο
Ρ
  


ΕΚ Ο . Κ  Ο Κ Ο
8
    

  
   
. 
Κ Ο Κ Ο.
   



    





Θ


Ε. )Κ . ΟΚ Ο Ε. )Κ . ΟΚ Ο
      
  
   

.
ΕΚ Ο Κ  Ο Κ Ο Κ Ο _ΜΕΚ Ο.
        


Κ/!Ο
&   Ρ.8#∗Κ8Τ ζ
Ρ

Ο   Ρ.8#∗
Ρ
Π

 ≅ΠΜ= Κ/!Ο ∀   

Ν   Κ8Ο

. ≅

  =_ΜΕ
Κ/!

Ο.

∆
.ΑΖΤ&ΣΤ∗(°(Υ#∃ξ∗+__+κ∀)ΨΖ∗+Ψ#∋(∀Τςσ∗∼∋≤Ψ)Τ(∗+κΞ#_/!&#Τ∗
Υ+/Ρς∀κ.∗(&Σ∗ΤΥ///Ψ#&Ξ+#∀ΤΥ///Ψ#/π∀&ΣΤ.
∀/%2




_
_Κ/!Ο_ΜΚ!Ο&
!∀Ν


2=__/!

.

Φ
ΑΖΤ/(ΤΨ#}!κ∀)ΨΖ∗+Ψ#∋()Ξ&#/(∋Ω_Μ≅8&Ξ,#σ∗ΨΖ=/!.∗(&Σ∗ΤΥ//π∀
/(ΤΨ#}!(#∗Ψ#∼∋∀&νΤς/∗,∗+&Ξ(#∗Ψ#∼∋∀&νΤς/∃#ΨΖΕ/!.
Τ
∀/%
≅8Μ_
8Μ≅.



_Κς∀κΟ.(#Ν_Τ(Ω&♦2♦Ρ_/!.
(#ΝΕ/!Τ(Ω&♦

 
♦Ε/!.

Γ.
ΑΖΤ/(ΤΨ#}!κ∀)ΨΖ∗+Τ()(|∗+ΤςΩ∗(%ΝΜΕ/)_ΤΚ/!Ο.Ξ)Τ(ο#Ψ#}!∗Ξ)Τ(Ω
(∀κ∀)ΨΖ∗+ΨΤ+#µΤςν


≈±/ρ∃#ΨΖΜ&Σ∗ΤΥ/Μ+#∀ΤΥ//π∀&ΣΤ,∗+,∀)∗(#σ∋≈
.
∀/%_Τ



Ο.Ω&_∗σ∗8Τζ


ζΤ

=
ζ_ΜΕ&#∝.(#Ψ…&…&
!∀Ν
2ΡΜ=/!.

!
. ΑΖΤ &ΣΤ ∗(° / (Υ# ∃ξ∗+ !  Ε_ +Μ κ∀) ΨΖ∗+ Ψ#∋ (∀ &# (|∗+ ΤςΩ∗(% Ν 
_/)Κ_Τζ


ΟΚ/!Ο.Χµ/Ψν∗(ΨΖ∃∗&Ξ/(#∋/π∀/µ/&ϒ/Τ|&Σ∗ΤΥ/Μ+#∀ΤΥ/&Ξ∃/ϒ)&
Τ#Τ(ο#Ψ#}!Τ_ΜΠΕ.
.
(#Τ_ΜΠΕ
_ΜΠΕ.


_ΜΕΤ(ΩΝ_/)Κ_._ΜΕζ


Ο_/)_/!
&2#∗_∀

Ν__!

 
 

…∀…
8   
 
 

_!

.

 .ΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀&#(|∗+ΤςΩ∗(%Ν_/)Κ_Τζ


ΟΚ/!Ο.Χµ/Ψν∗(Τ(ο#
Ψ#}!Ψ∋Τ#σ∗&ΣΤΨ#∼∋∀&νΤς/∃#ΨΖΝΕ/!Τ()/(#∋∗+ξ//(#∋&#/(#∋κ|∗+}
Τ♠Τ(ο#Ψ#}!Τ_.
.
∀/%ΝΕ_/)Κ_Τζ


Ο/)Κ_Τζ


Ο_ΜΕ/)Κ♦_Μ8Ο.
Ω&_∗σ∗_Τζ


_Μ8ζΤ_Μ__=ζ_Μ&#∝.+(#ϖ!κ|∗+∗(°

Ρ


Ρ

ζ
Τ

≅_
ζ_Μ.#∝.+(#ϖ!κ|∗+∗(°∗(ΤΤς)∗+(ƒ∗+(#ϖ!∗Ξρ∃ΞΤ
Ρ

.
.()/µ//(∋ρ}∗ΨΖ∗+Ψξ/!Τ,#/µ/(|∗+ΤςΩ∗(∀∋%
ΘΥ
Ε. Κ . Ο 
  

 
Κ/!ΟςΥ

.#∗ Κ. . Ο
Ρ
 


 
Κ/!ΟΥ
≅.#∗Κ8. . Ο ≅. Κ8. . Ο
   

#
ΕΚ Ο _ΜΕΚ Ο _Κ Ο
. .
    
 

 
    

/π∀κ∀)ΨΖ∗+∃Ξ%
_  _ Κ Ο.
   
     

,Ο

.#∗ Κ. . Ο  Κ8. . Ο
Ρ ≅
   
 
 
    
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)Κ8. . Ο )Κ8 Ο
Ρ ≅
    
 
 
     


    

∆. ΑΖΤ /(Τ Ψ#}! / (Υ# ∃ξ∗+ !  __+ κ∀) ΨΖ∗+ Ψ#∋ ()Ξ Τ() (|∗+ ΤςΩ∗( %
Ε. )Κ. . Ο
Ρ
  


 
Κ/!Ο.ρ

_.


Χµ/Ψν∗(∃#ΨΖΜ&Σ∗ΤΥ/Μ+#∀ΤΥ/Μ∃/(⁄/(θ#Τς)∗+/µ/
Τςο∗+(ξ∀∋%
∀Ο τΤ(ο#Ψ#}!ΤΕΚΟ.
,Ο (#(∀κ∀)ΨΖ∗+∃Ξ_
_
.
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♠(|∗+ΤςΩ∗(
Ε. )Κ. . Ο
Ρ
  


 
Κ/!Ο



_. . Κ. .Ε Ο _. . Κ Ο _. . Ε. ≅_
Ρ Ρ 
  
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   
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
 
 
. 8. .ΜΕ __Κ Ο Κ Ο
 
 
 
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.
∋/(♣∗+Τ°+#∀ΤΥ/∗+ξ//(#∋&#/(#∋κ|∗+Τς⁄/Τ)ΨΖ.


. 8.ΜΕ._ _ΜΚ Ο.

   

     

∋/(♣∗+Τ°/(⁄/(θ#∗+ξ//(#∋&#/(#∋κ|∗+Τς⁄/Τ)ΨΖ.
,Ο (#(∀κ∀)ΨΖ∗+∃Ξ_

. 8.ΜΕ. ≅ _Μ. ≅

       
ΚΟ.



Ε.)ΨΖ/π∀!ΖΤ&ΣΤ,#∗Τ(#σ∗Τ()Τ(ο#+#∀∗Τ()Ψν∗(∃∋ΣΤ%
8. Κ8. . Ο
  


Κ/!Ο.
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ο###
♠(|∗+ΤςΩ∗(
8. Κ8. . Ο
  


Κ/!Ο
∀/%
8  8. Κ  Ο Κ Ο
.
     

 

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.

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Η9
ζ



Μ&#





Μ%ΤΥ∗+Υκ∀)ΨΖ∗+
ζ∋/)∗∃υ/∃Ν)%




ΜΚ%!Μ!%+Ο
ζ(#/()ΨΖ+#∗/π∀∃Ν)


%
.
 
 

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ζ∋Ψ/()∃ρΨΖΝ♣∗+&#&Σ∗ΤΥ/&Τ(ΩΤ∀/%2








Κ∗∋,∋∗+∗(&_Ο
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 

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& ∀
2
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!∀Ν
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7
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 (#Τ_Τ(Ω
_
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) _
_
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.ϑ<
(#Τ(∗(Μ,∋∗+∗(&ΣΤ&
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6(∀κ∀)ΨΖ∗+∃Ξ%ΚΤζΟ
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Ο
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Ο

∃4?%≅Α=ΒΒΧ∆
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κ∀)ΨΖ∗+/π∀/)∗∃υ/Τς)∗+/µ/Τςο∗+(ξ%

.#∗
. .
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Ε.8. . _
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Ε.#∗Κ8. . Ο
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Κ/!Ο.

.
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Ε.#∗Κ8. . Ο

 


 
Κ/!Ο.
/Ο Τ_
_
_
.#∗
. .
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ΜΕ Ε.#∗
Ε.8. . _
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Ζ∗+/π∀/)∗∃υ/.
ο###
6(|∗+ΤςΩ∗(κ∀)ΨΖ∗+/κ∗+%
.#∗Κ . Ο
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6(|∗+ΤςΩ∗(&Σ∗ΤΥ//κ∗+%

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 

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Τ∀∗ 

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Κ Ο
8
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_.#∗Κ. . Ο
8
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_ Κ Ο  
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Τ_
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Κ Ο

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6(|∗+ΤςΩ∗(/κ∗+%Ν2./)Κ
.

 

Ο.
6(|∗+ΤςΩ∗(&Σ∗ΤΥ/%&2.
.#∗Κ . Ο

  

.
6(|∗+ΤςΩ∗(+#∀ΤΥ/%∀2.

. Κ . Ο
 
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

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616Φ6%
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(#&ΣΤκ∀)ΨΖ∗+Ψ#∋()ΞΤ♠Ν

Ψ∗Ν

Τ(ΩΤ|∗+♣∗+&♣)#∋&ΣΤ/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋
Τ♠ΑΨ∗Κ/(±≡Ν

&ΞΝ

∃Ξ(Ω∗(/(#∋&∋∗++//π∀Α&Ξ∃σ∗Τς⁄/3Χ
(ο#+#∀∗∗+υ∗∗(Τ&ΣΤκ∀)ΨΖ∗+Ψ#Τ♠Ν

Ψ∗Ν
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,∗+Τ(ο#+#∀∗&ΣΤ/(∋ρ}∗ΨΖ∗+Τς∗
Ψ∋Τ♠ΑΨ∗
/
;
, ;
∴ ]  ] 
Ε
Μ

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ζ(#&ΣΤΨ#Τ♠%



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ζ(#&ΣΤΨ#Τ♠%Ν_




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 ,Ο(ο#+#∀∗&ΣΤΨ#Τ♠,#σ∗Ψ∗ 2Ψ∗2Τ()/(#∋κ|∗+.
 /Ο∗(&Σ∗ΤΥ/Τς∋∗+,Ω∗(/π∀&ΣΤΤς)∗+/∋∀

,α

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Τς∗Τ♠Ψ∗−Ψξ/!ΖΤ+/≅_
_
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   



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_
(Τ(°∗+Τ(ο#+#∀∗ Τ
 ∗+∼∋ρΤυ/Τ∀!∋ΤΤ∀Τ∗(Ψξ/


 /ΟΣ∗ΤΥ/Τς∋∗+,Ω∗(/π∀&ΣΤ%
Τ,
 
∆ΑΖΤ&ΣΤκ∀)ΨΖ∗+&#(|∗+ΤςΩ∗(%
_.#∗Κ. . Ο

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Κ/!Ο.Ω!Τ(ο#Ψ#}!&ΣΤΨ#∼∋∀
&νΤς/∃#ΨΖΝΕΚ/!Ο∃∗Τ(♣(∀#Τ()/(#∋κ|∗+.
ο###
/µ/ Τ(ο# Ψ#}! &ΣΤ Ψ# ∼∋∀ &ν Τς / ∃# ΨΖ Ν  Ε/! Ψξ/ Νµ/ Ψν∗( ,# (|∗+ ΤςΩ∗(%

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ΣΤΨ#∼∋∀&νΤςΝΕ/!∃∗(∀#Τ()/(#∋κ|∗+

.ΣρΤ∀/
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 

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8.#∗Κ_ . Ο
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,Ο()∗+Τ(ο#+#∀∗∗+υ∗∗(ΤΨ}&ΣΤΨ#Τ♠&νΤς/∃#ΨΖΝ


8_
 

Κ&Ω&_Ο
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Κ/!ΟΨ∗&νΤςΝ


8Κ/!Ο∃Ξ%]

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  
Κ Ο
8_ _ Ρ_

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.
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_
Ν

/!Τ()/(#∋κ|∗+ΜΤ∀/%
_ 

8.#∗Κ Ο  #∗
 Ρ
  


   Ο



  Ο

Ρ

 Ο




α(ƒ∗2
µ/(%ΣΤ∼∋∀%Ν_Τζ


8 

 
  

(ο#Ψ#}!Τ(♣∗(Τ♣∗+&#_Τ8ΚΟ
µ/(%Λ→κ⁄∗+!Υ#∃#σ∗(ϖ+#∀κΨΨ(&Ξ/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋.
ΣΤΨ#∼∋∀Μ♣∗+&#&ΣΤ/(∋ρ}∗ΨΖ∗+Τς∗Ψ∋∼∋∀Α

&ΞΑ

.


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Μ&#






)&,µΙνο% ζ&ΣΤΨ#Ψξ/∼∋↔∗+Ψο∗+82

3



8

ΝΚ/





3

Ν

Α




Τ∀Τ∗(Ν

2/)ΚΤ

ζΟ/!&Ξ&

κ|∗+(∀ρ!
Κ(∗+Τ∗(&

Ο
   ζ(#ΤΤ

Τ∀Τ∗(Ν

2/)ΚΤ

ζΟ/!&Ξ&

κ|∗+(∀ρ!
Κ(∗+Τ∗(&

Ο
Λ∀∋Ψ&↓(Ω∗(/π∀&ΣΤΤς)∗+(∗∃↓


/(∋∞ςθ#κ∀&Ξ)(Ω∗(&↓Ψ}Τ∗(Λ
∃↓
&ΞΥ
∃∗Α

∃↓
∗
ζΗ∋↔∗+Ψο∗+Ψ#Ψξ/%
Λ
∃↓
2ζΚ2Ν

ΟζΚ2


Ο82Ν




Η∋↔∗+Ψο∗+∃∗∗(Τ(#&ΣΤΨ#Τ♠Α

Ψ∗Α

ΨΥ#
Ν♣∗+∼∋∀Τς⁄/#∗Κ(Ω∗(Ο

∀Ν
2 #∗







   

 ς)∗+Τ(ο#+#∀∗



∼∋↔∗+Ψο∗+
∃∋∗∃Ξ∗2
 ς)∗+Τ(ο#+#∀∗

Τ€Τ(Ω∼∋↔∗+Ψο∗+∃∗∗(ΤΜ∗(°∗(ΤΤ∗(∗(Τςσ∗.

⊥_;/:


4Κ)ΛΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀Τ()(|∗+ΤςΩ∗(Ν8/)Κ≥Τζ≥≅Ο.∗(∼∋↔∗+
Ψο∗+!Ξ&ΣΤΨ#Ψξ/Τς)∗+Τ(ο#+#∀∗≅ΜΠΕ.

∃%.

 ℜκΞ∗+∗(Σ∗Τ(ρΜΤς)∗+Τ(ο#+#∀∗/(∋∞&ΣΤκ∀)ΨΖ∗+Ψ#Ψξ/∼∋↔∗+Ψο∗+82
 (∋∞κ∀)ΨΖ∗+/π∀&ΣΤ%  Κ,∗Ψƒ/ΤΤ∗(Ο
 ()∗+Τ(ο#+#∀∗≅ΜΠΕ≅/(∋∞ζ_ΜΠΕ
  ζΗ∋↔∗+Ψο∗+&ΣΤΨ#Ψξ/Τς)∗+≅∼∋↔∗+Ψο∗+&ΣΤΨ#Τς)∗+≅/(∋∞≅℘
828=
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2



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!&∋ ()∗+(,−./−−/−0/−12345678

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στυ
Η#χττ∗ϖωΙξ&,τ∗+&,ϕ

Η#χτωΙΘψτµΠ

5ζ,λ){#χ&|#

ι}Ι∼5ρ∗κ&,Υ&&
>ΒΜΝΟ>ΒΠ>
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6(|∗+ΤςΩ∗(&Σ∗ΤΥ/%&2#∗ΚΤζΟ/!
 Υ2#χτωΙΘψτµΠ

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Ρ

Ο/!.(ο#Ψ#}!Τ(♣
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!
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Ε 
Κ/!Ο∃∗Τ(♣,∀Τ()/(#∋!.
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Ε 
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ΤςΩ∗(∀∋%

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3
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._. Κ Ο

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Ε 
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

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_&ΞΤ_
ζ(#Τ_


_.#∗ _

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Μ&ΣΤ,υΤΨ∋κ∀)ΨΖ∗+Τ♠&νΤς,#σ∗κ|∗+.ΣΤΨ#∼∋∀&νΤς
ΝΕ/!∃∗Τ(♣∗(ΤΤ()/(#∋!Μ∼∋∀&νΤς∗Ξρ∃∗Τ()/(#∋κ|∗+.∀/∗+∀ρ&ΣΤ
∼∋∀&νΤςΝΕ/!∃∗Τ(♣__=Τ()/(#∋κ|∗+ΜΤς)∗+Υ__=∃∗&ΣΤ∼∋∀&νΤςΝΕ/!Τ(Ω
/__8∃∗&ΣΤ∼∋∀&νΤςΨΤ()/(#∋κ|∗+.ΣρΤ(ο#Ψ#}!&ΣΤ∼∋∀&νΤςΝΕ/!∃∗Τ(♣
__=∃Ξ%

≅_ Ε


  
&#__8.

 __8 Ρ_8  Ρ_≅
≅_ Ε ≅_ ≅_


    
ΚΟ.

!&∋ ()∗+(,9/.:/ 23456;<−78


&#Λ
Α∀Ν
Λ
Α#∗
Τ∗(∗(κ∗+ΕΤςσ∗.

χ&ρ<&,∼ΙΕ5Ε5Ε∆5ΦΕ5Φ5Γτ}∆



9!
ΖΞεϕ∋>Λφ6∋/ΖΩΜ//


=0=Ξ=
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ς)∗+!ΖΤ/(∋∞&ΣΤ∼∋∀∃#ΨΖΝ∃∗.
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Τµ/(∗Μ∀,/∗ζ∀,/Τ∗.ζ


Τς)∗+Ψ%


_Μ∀,/.
Ω!Υ∃∗&ΣΤ∼∋∀∃#ΨΖΝΤς)∗+Τ(ο#+#∀∗


Κ∃∗Μ∃∗Μ()/(∗+∃∗∗Ξ)Ο


∼Ι Ε 6(|∗+ ΤςΩ∗( κ∀) ΨΖ∗+ /π∀ !ΖΤ &ΣΤ κ∀) ΨΖ∗+ Ψ#∋ ()Ξ / κ∗+ Ν  Ρ/)Κ_

Τ
ζ

ΟΚ/!Ο.#ΨΖ/π∀&ΣΤ(#(∀κ∀)ΨΖ∗+,∗+ΚΡ_
_
Ο∃Ξ
 2.≅/!. 
.≅/!.  .8Μ8/!.  .8Μ8/!.
∼ΙΦΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()ΞΜΤς)∗+Τ(ο#+#∀∗(±Τ&ΣΤΤ(/(#ϖ∗Ψξ/≅_κ∀)ΨΖ∗+.
(∋Ωκ∀)ΨΖ∗+/π∀&ΣΤ∃Ξ
 2..  .≅_.  ._ΜΕ.  ..
∼ΙΓΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()Ξ/(|∗+ΤςΩ∗(κ∀)ΨΖ∗+∃ΞΝΕ/)Κ

Τζ

≅ΟΚ/!Ο.
Σ∗ΤΥ//π∀&ΣΤ(#/∃#ΨΖΝ≅/!∃Ξ
 2.ΕΜ/!.
.

ΕΜ/!. .

ΜΕΡ/!. .ΜΕΡ/!.
∼ΙΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()Ξ/(|∗+ΤςΩ∗(κ∀)ΨΖ∗+∃ΞΝΕ/)Κ

Τζ


.  .&_ΜΡ!∀_Μ8=/!

.
 .&Ρ!∀8=/!

.  .&_ΜΡ/!∀8=/!

. 
∼ΙΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀(#&ΣΤ/∃#ΨΖΝ

≅/!Τ(Ω &Σ∗ΤΥ//π∀&ΣΤ∃Ξ&


8_/!Μ(#&ΣΤ∼∋∀&νΤς/∗,∗+Τ(Ω&Σ∗ΤΥ//π∀&ΣΤ∃Ξ&

Ε_/!.∗Υ/π∀κ∀)ΨΖ∗+
Ψ#∋(∀∃Ξ
 2._

ΚΟ. .Ε

ΚΟ.  .

ΚΟ.  ._ΚΟ.
∼Ι ΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋(∀Τςσ∗∼∋≤Ψ)κΞ#8_/!.(#&ΣΤ&νΤςΝ_/!Τ(Ω&ΣΤ
/&Σ∗ΤΥ/∃Ξ&_


/!.(∋Ωκ∀)ΨΖ∗+/π∀&ΣΤ∃Ξ
 2..  ._ΜΕ.  ._Μ.  .Ε.

Ζ∃∗+#∀ΤΥ///Ψ#/π∀/(ΤΨ#}!,∗+
 2.ΜΕ!

.  .Ε!

.  .Ρ≅Μ!

. .ΡΜ≅!

.
∼ΙΑΖΤ/(ΤΨ#}!κ∀)ΨΖ∗+Ψ#∋()Ξ.#Τ(ο#Ψ#}!Τ

∃#ΨΖ/π∀/(ΤΨ#}!∃ΞΝ

≅/!
&Ξ&

Ρ_

/!.Τ#Τ(ο#Ψ#}!Τ

/∃#ΨΖΝ

≅

/!&Ξ&

Ρ_

/!.#σ∗ΨΖ&ΞΤ∗


.  .


2≅

.  .

2≅


.  .

2≅

.





8
∼Ι ΑΖΤ/(ΤΨ#}!Α/(∋ρ}∗ΨΖ∗+Ψ∋Τςσ∗!ΖΤΨο∗+Τς∗&#ΤΥ/ΨΖκΞ#Ρ_/!&Ξ
ΤΥ/ΨΖ+/8ς∀κ.Ω∗(/(#∋6/π∀/(ΤΨ#}!ΑΤςσ∗!ΖΤΨο∗+Τ(∗+/ΥΨν∗(∗!Τς)∗+
!Τ(∗+(Ω∗(Τς∗κ∀)ΨΖ∗+Ψ#∋()Ξ&#,#σ∗ΨΖ&Ξ/(∋Ω∃∗∃ξΤ∃Ξ
 2.8_/!_ΜΕ.
.8_/!ΜΕΠ. .8_!_ΜΕ. .ΜΕ!ΜΕΠ.
∼Ι∆6(|∗+ΤςΩ∗(&Σ∗ΤΥ//π∀!ΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()Ξ∃Ξ&_/)_ΤΚ/!ΟΜ&#ΤΨ)
,∗++#ρ.Ξ)Τ(ο#Ψ#}!ΤΡΚ∃Ξ/(∋Ωκ∀)ΨΖ∗+ΟΜ&ΣΤ/∃#ΨΖ∃Ξ
 2.≅/!.  .≅/!.  .


)&#&Σ∗ΤΥ/.
∼Ι∆ΓθΤ(ν,#}∋κ#ℜ∗,#∗Τ(#σ∗/π∀&Σ∗ΤΥ/Τ()∃#ΨΖΤς)∗+κ∀)ΨΖ∗+Ψ#∋()Ξ/
κ∗+∃Ξ
 2.Ψο∗+∀ς∀,)∃. .Ψο∗+Τς∗.
.Ψο∗+∃#. .Ψο∗+(ρ,)∃.
∼Ι∆θΤ(ν,#}∋κ#ℜ∗,#∗Τ(#σ∗/π∀+#∀ΤΥ/Τ()∃#ΨΖΤς)∗+κ∀)ΨΖ∗+Ψ#∋()Ξ/
κ∗+∃Ξ

2.Ψ)∗Τ(∗+. .Ψο∗+Τ(∗+. .Ψο∗+(Ω∗(#∗..Ψο∗+∀ς∀,)∃.

∼Ι∆!(ƒ∗(µΤ,#}∋&ϑ.#σ∗ΨΖκ∀)ΨΖ∗+/π∀/)∗∃υ/∃Ν)(∗+∗((∗+Ψ∗

2.Τ∗Υκ∀)ΨΖ∗+.   .&Σ∗ΤΥ///Ψ#.
 .+#∀ΤΥ///Ψ#.    .ΨΖ∗+∗♥∗+//Ψ#.
∼Ι∆ς)∗+(|∗+ΤςΩ∗(κ∀)ΨΖ∗+Ψ#∋()ΞΝ2/)Κ

Τζ

ΟΜ/µ/Ψ#∃ξ∗+

Μ

ΜΚ

Τ
ζ

Ο∃Ξ∗(∗+Ψ#∃ξ∗+Τς∋∗++#∀∗/()(ϒΝµ/Ψν∗(
2.∃#ΨΖ&Ξ(∀,∀∗Ψ∋.   .,#σ∗ΨΖ&ΞΤς∗+Τ(µ#κ∀)ΨΖ∗+.

.,∗+ΨΖ∗+∗♥∗+/π∀&ΣΤ(#∼∋∀&νΤς/∗,∗+.
.,∗+Τ(∗♥∗+/π∀&ΣΤ(#∼∋∀&νΤς/∗,∗+.
∼ΙΕΦ#∃ξ∗+∗Ξ)∀∋ΨρΤ♥∗++Ψ#(#Τ♥∗++Ψ#,#σ∗ΨΖκ∀)ΨΖ∗+Ψ#∋(∀/π∀
/)∗∃υ/∃Ν)
 2.|∗♥∗+/π∀/)∗∃υ/.   .Ζ∗+∗♥∗+/π∀/)∗∃υ/.

.Σ∗ΤΥ///Ψ#.   .(∗♥∗+/π∀/)∗∃υ/.
∼ΙΕΓς)∗+κ∀)ΨΖ∗+Ψ#∋(∀ΨΖ∃∗+#∀ΤΥ//π∀&ΣΤ

2.+#!(#ΨΖ∃∗/π∀&Σ∗ΤΥ/Τ♥∗+. .Τ♥∗+(#ΨΖ∃∗/π∀&Σ∗ΤΥ/Τ♥∗+.
 .(∗+Τ(∀ρΨω#.   . Τ♥∗+Μ +#! Τρ Τ(∋Ζ/ &Σ∗ ΤΥ/ Ψ∋ ∃∗ (∀ρ
∗(°.
∼ΙΕΖ∗+∗♥∗+&ΞΤ(∗♥∗+/π∀!ΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()Ξ&#,#σ∗ΨΖ2↓,∗+∗(∀∋
(#∃#ΨΖ/π∀∗,∗+
 2.Ν

2
.  .Ν2.  .Ν


2
. .Ν

2

.
∼ΙΕ!#Τ(ο#Ψ#}!(#&ΣΤΤ(/(#ϖ∗κ∀)ΨΖ∗+Ψ#∋(∀/&Σ∗ΤΥ/,∗+&Σ∗ΤΥ///
Ψ#Τ(Ω&ΣΤ/∃#ΨΖ,∗+,∀)∗(#σ∋≈
 2.2


∼ΙΦΑΖΤ&ΣΤκ∀)ΨΖ∗+Ψ#∋()ΞΤ()Τ(ο#+#∀∗/(|∗+ΤςΩ∗(Ν2./)

Κ
Τ

ζ

≅ΟΤ(Ω
ΨΖ∗+∗♥∗+&ΞΤ(∗♥∗+/∗+κ∀)ΨΖ∗+Τ∋∗()Ξ∗&#Τ∗Υ+/
 2.




.  .




.  .


8

.  .


_ΜΕ

.

#∗

Κ

ΤΟ.#µΤςν∃∗∗(Τ/π∀
Τ(∗♥∗+∃Ξ
 2.


_
.  .
_
.  .
_
.  .
_
.
∼ΙΦΦ6(|∗+ΤςΩ∗(κ∀)ΨΖ∗+/π∀!ΖΤ&ΣΤ/κ∗+Ν2/)

Κ

Τζ

8Ο.(ƒ∗Τ∃∋Σ∗
&ϑ.
 2.ΣΤκ∀)ΨΖ∗+&#,#σ∗ΨΖ2. .ΣΤκ∀)ΨΖ∗+&#,#σ∗ΨΖ2.
 .ΣΤκ∀)ΨΖ∗+&#,#σ∗ΨΖ2. .ΣΤκ∀)ΨΖ∗+&#(∀,∀∗Ψ∋

8.


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