usinenumerique.py

Created on March 06, 2025

547 Bytes

Sans frottement :
Z = somme
 ->   ->
ZF = ma
 ->  -> 
ZF . y = mg = may => g=ay

Uy(t) = Uy0 + Vy0 t + 1/2 gt^2

avec frottement

b = alpha
 ->  -> 
ZF . y = mg - b Vy = may
                 .
=> mg - b Vy = m V(t)
     . 
=> m V(t) + b Vy(t) = mg
   .
=> V(t) + b/m Vy(t) = g

On pose k = b/m
   . 
=> V(t) + k Vy(t) = g

-> homogene
. 
Vy(t)+k Vy(t) = 0
.
Vy = -kVy
   .
=> Vy/Vy = -k

=> lr'(Vy)=-k

on intègre

=> lr(Vy)=-kt+cst

Vy = e(-kt+cst) = e(-kt)e(cst)
= De(-kt)

2 Solution particulière

0+k Vy = g
=> Vy = g/k

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