Chapitre 4 :Oscillateur harmonique

! # !$ )* • +

=

+ω

% ,

= −

'

- # !$

•

+

=

=' " & ω

(

+

%

&

− .

=

# !$

• •

=

'

+

+

% &

%$

/

=

='⇔ +

=− +

= ( (

='⇔ +

='

=' #

#

='

"

) "

"

=

= "2

%1

0

3

% +ω(

&

=' ω

" =α⋅

+β⋅

−ω

ω4 + "ω4 + ϕ % 5ω

= = $

+

ω4 5ϕ

"ω4 + ϕ

" =

,

" =− ω

= =

(

(

+ =

=

(

(

=

(

(

( (

( (

(

=

(

(

ω(

!$

= ω(

&

"ω4 + ϕ

"ω4 + ϕ = (

4

(

(

ω(

(

"ω4 + ϕ

"ω4 + ϕ

ω(

ω(

π 0ω %

#

%

% 4

(

=

(

(

ω(

=

(

(

(

"ω4 + ϕ =

ω( ×

(

(

(

.

ω(

"("ω4 + ϕ (

− =

5

=

"("ω4 + ϕ

(

% " = " 0ω =

"−ω4 − ϕ " −ω4 − ϕ " 0ω

"

%

)

%

% $

%

)*

7

⊥ =− " −

'

⋅ =−

⋅

= −µ ⋅ = −µ ⋅ ⋅ " + % % + + + = 0"

%

(λ =

µ

. ω '( =

%

+ (λ ⋅ + ω '( = '

!

−µ⋅ ⇔ +

=−

8

/$

%

.

% & +

ω'

=

µ

+

='

ω' ω' = (λ µ

% ⋅ + ω '( = '

6

='

( )*

+

+

='⇔

+

+

$ %

λ=

. ω' =

(

=

.

) "

"

=

=

0

µ

3 9

% $ + (λ ⋅

%

+ ω '(

∆= λ − ω (

='

( '

∆ > ' "λ > ω ' 5

= −λ ± λ − ω (

5(

" =

+

(

( '

(

∆ = ' "λ = ω ' 5

(




(

='⇔

ω' (

+

+

&

='

∆ = λ( − ω '( = − ω ( 5(

= −λ ±

" =

−λ4

=

−λ 4

−∆ = −λ ± ω ( "α × − ω 4 + β ×

ω4 +

"

−λ

=

=

%

ω4

ω4

"ω4 + ϕ (π

ω " " +

δ=

=λ

>> " ∆

≈

(π

%

% $

% % # " −λ

" =

" = −λ ⋅

%

%$ >>

4

%

% :

%

&

"ω4 + ϕ −λ

−λ

"ω4 + ϕ −

= −λ " −λ "ω4 + ϕ − ω × >> ⇔ δ = λ