sujet

y00 (t)+3y0(t) + y(t) = cos(t)
y(0) = 2
y0(0) = 0
t= 0 t= 100

¨x(t)+x(t) = 0
v(t) = ˙x(t)
¨x(t) + x(t)=0 ⇔˙x(t) = v(t)
˙v(t) = −x(t)
¨x+ω2x= 0

ω= 1
x(t= 0) = 1 ˙x(t= 0) = 0
x(t= 0) = 0 ˙x(t= 0) = i i ∈ {−3. . . 3}, i 6= 0
¨x+ω
Q˙x+ω2x= 0
ω= 1 Q= 20,10,1,0.5 0.25
x(t= 0) = 1
˙x(t= 0) = 0
Qc
Q
Q= 10,0.5
0.25
x(t= 0) = 0 ˙x(t= 0) = i i ∈ {−1,1}
˙x(t= 0) = +1 ˙x(t= 0) = −1
m l
θ(t)

g
θ= 0
¨
θ+ω2sin θ= 0
ω=rg
lω= 2π s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 13 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 8 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 4 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 1 rad.s−1
0 2
θ(t= 0) = 0 ˙ θ(t= 0) = 4 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 8 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 12 rad.s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 13 rad.s−1
2ω
2ωdt
dθ
θ
θ=π

¨
θ+α˙ θ+ω2sin θ= 0
0 20
α= 0.3s−1
θ(t= 0) = 0 ˙ θ(t= 0) = 16 rad.s−1
α