Dyuamel integrali

Dyuamel integrali

Murakkab shaklli ta’sirni kichik zinasimon (bosqichli) ta’sirlarga yoyish mumkin.

u₁(t)














0  2 3 4 5 t

t - hisob uchun olingan payt,

 = k ·   - noldan (boshidan) hisoblanayotgan vaqt (k - butun son),

k     (uzluksiz vaqt),

 d.

Jamlash tamoyiliga asosan, kuchla- nish bo’yicha o’tkinchi xarakteristikasidan - h_u(t) - foydalanib va integralga o’tib, Dyuamel integrali yordami bilan zanjirning reaksiyasini u₂(t) olish mumkin (isbotsiz):

1-shaklda: u₂(t) = u(0)*h_u(t)+ u′(τ)* *h_u(t-τ)dτ

2-shaklda u₂(t) = u(t)*h_u(0)+ u(τ)* *h_u′ (t-τ)dτ

Eslatma: videoimpuls uchun 1-ifodada (1-shaklda) ikkinchi had nolga teng [u′(τ)=0, u=Const] va faqat 1- had qolyapti:

u₂(t) = u(0)*h_u(t) = U₀*h_u(t)

Jamlash integrali

f(t)

0 t






e ^-t t  0 uchun

f(t)=

0 t <0 uchun

1-yo’l: F(jω)=  e^-αt e^-jωt dt =

= e^-(α+jω)tdt= 

=

2-yo’l:F(jω) = F(p)/_p=jω =1/(p+α)/_p=jω = =1/(α+jω) .

|F(jω)| = F(ω) = 1/ –

amplitudaviy spektr

()

0

-90⁰

ψ(ω)= - arctg (ω/α) – fazaviy spektr

F()

1/