Travaux dirigés L1-S2 : Vibrations et ondes, optique géométrique

m k
l0O
L
g
z t
m g k l0L
T z t =T/8
m= 0,1g= 9,81 −2k= 100 l0= 0,2L= 0,05
1
x10
3−1
x(t)v(t)
0 2πsin2x π
m= 400
R1A1R2
A2
10 8 R1R2k1k2R1R2
k2k1= 40
A1A2
t= 0 A10,1
m
L θ (t)
t g
θ(t)
mL¨ θ+mg sin θ= 0
θ
sin θ'θ−θ3
3! +θ5 5!

sin θ θ (t)
ω0T0
g L
1 sin θ
T0m g L
T0g L
L T0= 1
T0= 2
ε L 1
k
x0x
−f~v f ~v x = 0
k/m =ω2
0
f/2m=γ
x(t) = Ae−γt cos (ωt −φ)
ω x (t) 0 <t<60
ω= 0,785 A= 5 γ= 0.1−1φ=π/3
m Ox x(t)
t O
Ox x(t)
k
Ox
ω0k m q
Ox
Ex(t) = E0cos(ωt)ω
Ox
x(t) =
x0cos(ωt)x0E0ω ω0q/m
x0ω ω ω0
x0
m k1
k2x1
x21
x1x2

mm
x
1x
2
k
1
x
1
k
1
k
2
x
x+=x1+x2
x−=x1−x2
x1(t)x2(t)
t= 0
x(0)
1
x2(0) = 0
x1(t)
x2(t)k2k1
cos(x) + cos(y) = 2 cos x+y
2cos x−y 2
cos(x)−cos(y) = −2 sin x+y
2sin x−y 2

Ox Ψ (t)O
v M x τ =x/v M
Ψ (t−τ) = Ψ t−x
v
u=t−x/v
∂2Ψ
∂x2−1 v2
∂2Ψ
∂t2= 0
Ψ = ϕ(x)f(t)
v21
ϕ(x)
d2ϕ(x)
dx2=1 f(t)
d2f(t)
dt2
−ω2ϕ(x)f(t)k=ω/v
Ψ1(x, t) = Ae−(2kx+3ωt)2
Ψ2(x, t) = Asin χx2−ωt
Ψ3(x, t) = Asin (kx −ωt) + Bcos (kx −ωt)
Ψ4(x, t) = Asin (kx)Bcos (ωt)
0,25
120
θ= 90 µ= 0,25 −1
x t = 0 x= 0
Ψ=0
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