25-mavzu. Davriy jarayonlar. Garmonik tebranishlar kinematikasi

Davriy jarayonlar. Garmonik tebranishlar kinematikasiga oid masalalar

25-mavzu: Davriy jarayonlar. Garmonik tebranishlar masalalari

1-masala: Garmonik tebranish parametrlari

x = A sin ω(t + τ) tenglama bilan berilgan tebranishning davri, chastotasi va boshlang'ich fazasi aniqlansin.

Asosiy formula: x = A sin(ωt + φ₀)

A (amplituda, m):

ω (rad/s):

τ (s):

2-masala: Boshlang'ich faza va vektorli diagramma

x(t) = A cos(ωt + φ) qonun bo'yicha tebranayotgan nuqta uchun boshlang'ich fazani toping.

Asosiy formula: φ = arccos(x(0)/A)

A (amplituda, m):

x(0) (boshlang'ich siljish, m):

ω (rad/s):

3-masala: Maksimal tezlik va tezlanish

Amplitudasi A, davri T bo'lgan garmonik tebranayotgan nuqtaning maksimal tezlik va tezlanishini toping.

Formulalar:
v_max = Aω = A(2π/T)
a_max = Aω² = A(2π/T)²

A (amplituda, m):

T (davr, s):

4-masala: Faza farqi va superpozitsiya

Ikki garmonik tebranish x₁ = A₁sin(ωt + φ₁) va x₂ = A₂sin(ωt + φ₂) yig'indisini toping.

Formulalar:
A = √(A₁² + A₂² + 2A₁A₂cos(φ₂ - φ₁))
φ = arctg((A₁sinφ₁ + A₂sinφ₂)/(A₁cosφ₁ + A₂cosφ₂))

A₁ (m):

A₂ (m):

φ₁ (rad):

φ₂ (rad):

ω (rad/s):

5-masala: Tezlik va tezlanish funksiyalari

x = A sin(ωt + φ) tebranish uchun tezlik va tezlanish tenglamalarini chizing.

Formulalar:
v(t) = Aω cos(ωt + φ)
a(t) = -Aω² sin(ωt + φ)

A (amplituda, m):

ω (rad/s):

φ (rad):

6-masala: Energiya taqsimoti

Garmonik tebranishda kinetik va potensial energiyalarning vaqtga bog'liligini toping.

Formulalar:
E_k = ½mv² = ½mA²ω²cos²(ωt + φ)
E_p = ½kx² = ½mω²A²sin²(ωt + φ)
E = E_k + E_p = ½mA²ω²

m (massa, kg):

A (amplituda, m):

ω (rad/s):

Mavzu ma'lumotlari

Kategoriya: Masala
Mavzu: 25-mavzu. Davriy jarayonlar. …
Masalalar soni: 10 ta
Daraja: O'rta

25-mavzu. Davriy jarayonlar. Garmonik tebranishlar kinematikasi