PROBLEME 1 : Charge électrique plongée dans un champ

q=−e m
z~ B=B~ez
(x0y)
t
x(t) = v0
ωc
sin(ωct)
y(t) = v0
ωc
(1 −cos(ωct))
z(t)=0
v0t= 0 ωc
( ˙x(t),˙y(t),˙z(t)) t
(¨x(t),¨y(t),¨z(t)) t
~
F=q~v ×~ B
ωce m B
T
~
F=q~v ×~ B t1t2
−→

k `0
m
~g =g ~ez
z
~
Fr=−k(z−`0)~ez
z(t= 0) = z0t= 0
z(t) = z0cos(ωt) + zeq(1 −cos(ωt))
ω zeq
~
Ff
~
Ff=−η˙z ~ezη
η
k z(t= 0) = z0˙z(t= 0) = 0
α=η
2m
z(t)t→ ∞