oscillations.py

Created by alten01

Created on December 20, 2023

680 Bytes

LE RESSORT
F=k(l1-l0) en N/m 
[k]=[F]/[L]=MT^-2 en N/m en kg/s^2
dapres le pfs P+F=0
soit k=mg/l1-l0



OSCILLATION LIBRE ps de frottements
dapres le pfd P+R+F=ma
soit x..+lx=0
[k/m]=T^-2



pulsation propre : w0^2 = k/m
periode propre : T0 = 2pi/w0 
= 2pisqrt(m/k)



OSCILLATION AMORTIE
regime aperiodique :
lambda > w0
x(t)=Aexp(x1t)+Be(x2t)

regime critique :
lambda = w0
x(t)=(A+Bt)exp(xt)

regime pseudoperiodique :
lambda < w0
x(t)=(Acos(wt)+Bsin(wt))exp(-lambdat)
avec w0=sqrt((w0^2-lambda^2))

dapres le pfd P+R+F+f=ma
sur Ox: -F+f=max
-kx-hx.=mx..
mx..+hx.+kx=0
attenuation:2lambda=h/m
x..+2lambdax.+w0^2x=0
X^2+2lambdaX+w0^2=0
delta=4(lambda^2-w0^2)

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