27-mavzu. Garmonik tebranishlar dinamikasi

m massali moddiy nuqta ν chastota bilan garmonik tebranadi. Amplituda A. Tezlik, maksimal kuch va to'liq energiya aniqlansin.

Formulalar:
v = ±2πν√(A² - x²)
F_max = 4π²ν²mA
E = 2π²mν²A²

m (massa, kg):

ν (chastota, Hz):

A (amplituda, m):

x (siljish, m):

Uzunligi l, massasi m₃ bo'lgan tayoqcha uchlariga m₁ va m₂ massali sharchalar mahkamlangan. Tebranish davri T aniqlansin.

Formula:
T = 2π√[(3m₁ + 3m₂ + m₃)l/(6(m₂ - m₁)g)]
J = (1/12)l²(3m₁ + 3m₂ + m₃)
l_c = (m₂ - m₁)l/(2m)

m₁ (kg):

m₂ (kg):

m₃ (tayoqcha, kg):

l (uzunlik, m):

Uzunligi l, massasi 3m₁ bo'lgan tayoqchaning uchiga diametri d=0.5l, massasi m₁ bo'lgan obruch mahkamlangan.

Formula:
T = 2π√(7l/6g)
I = (7/8)m₁l²
l_c = 3l/16

m₁ (obruch massasi, kg):

l (tayoqcha uzunligi, m):

Massa m, prujina konstantasi k bo'lgan prujinali mayatnikning to'liq tahlili.

Formulalar:
T = 2π√(m/k)
ω = √(k/m)
F = -kx (Guk qonuni)

m (massa, kg):

k (prujina konstantasi, N/m):

A (amplituda, m):

Uzunligi L bo'lgan oddiy mayatnikning kichik tebranishlari.

Formulalar:
T = 2π√(L/g)
ω = √(g/L)
θ_max = A/L (kichik burchaklar uchun)

L (uzunlik, m):

m (massa, kg):

θ₀ (boshlang'ich burchak, rad):

Garmonik tebranishdagi energiya almashinuvi va fazalar tahlili.

Formulalar:
E_k = ½mv² = ½mω²A²cos²(ωt + φ)
E_p = ½kx² = ½kA²sin²(ωt + φ)
E = E_k + E_p = ½kA² = const

m (massa, kg):

k (N/m):

A (amplituda, m):

27-mavzu: Garmonik tebranishlar dinamikasi masalalari