Coursoscforcee_001

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Abdelkrim Salem I / Cas d’un oscillateur mécanique : 1°) Etude expérimentale :

moteur ( excitateur) règle graduée liquide 2°) Etude théorique : a) Equation différentielle : ♦ Système = { S } ρ ρ ρ ρ Bilan des forces extèrieures : P , T , f , F ρ ρ ρ ρ ρ R.F.D. : P + T + f + F = m a Projection sur (x’x) : - k x - hv + F = m D’où : kx + h

dx dt

+m

d2x dt 2

= Fmsin( ω t )

équilibre O (S)

d2x dt 2

x

(*)

Cette équation différentielle admet comme solution : x = xmsin ( ω t + ϕ ) pulsation du moteur ( excitateur ) ρ kx = k xmsin ( ω t + ϕ ) V1 ( k xm , ϕ ) h

dx dt

m

= h ω xmsin ( ω t + ϕ +

d2x dt

2

π ) 2

= m ω 2 xmsin ( ω t + ϕ + π )

Fmsin( ω t ) ρ ρ ρ ρ (*) ⇒ V = V1 + V2 + V3

ρ π V2 ( h ω xm , ϕ + ) 2 ρ 2 V3 ( m ω xm , ϕ + π ) ρ V ( Fm , 0 )

1

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