Berilgan: K=125 N/m t=8s N=5 m=? Yechilishi

Javob: D) 5.
27.5. Moddiy nugtaning tebranish gonuni 𝑥 = 0.03 sin

2𝜋𝑡
ko’rinishda berilgan. Uning T = 3T/4
𝑇
paytdagi siljishi modulini toping (m).
A) 0.05 B) 0.04 C) 0,03 D) 0.02
Berilgan:
2𝜋𝑡
𝑥 = 0.03 sin
𝑇

Τ =
|𝑥| =?

Yechilishi: Berilgan garmonik tenglamada vagtning o'rniga berilgan givmatini go’vamiz:

2𝜋𝑡
|𝑥| = 0.03 sin = 0.03 sin
𝑇
Javob: C) 0.03.
2𝜋 3𝑇
⋅ = |−0.03| = 0.03 𝑚
𝑇 4

27.6. Nugtaning harakar tenglamnasi 𝑥 = 0.3 sin 0.1𝜋𝑡, ko'rinishda yoziladi.Harakatning qandayligi va uni tavsifiovchi kattaliklarni aniqlang.

1. 
   radiusi 0,3 bo’lgan aylana bo'ylab tekis harakat, chizigli tezligi 0.1m/s.
   
2. 
   Tebranma harakat, amplitudasi 3 sm, chastotasi 0,1 Hz.
   

C tebranma harakat, amplitudasi 30 sm, davri 20 s.
D) radiusi 30 sm bo'lgan aylana bo'ylab tekis harakat, aylanish davri
2,0 s.
Yechilishi: Berilgan harakat tenglamasiga asosan:
𝑥_𝑚 = 0.3𝑚 = 30𝑠𝑚; 𝜔 = 0.1𝜋.
Tebranish davrini siklik chastotaga bog’lanish fodasidan t topamiz:
2𝜋 2𝜋

Τ = = = 20 𝑠 𝜔 0.1𝜋
Javob: C) tebranma harakat, amplitudasi 30 sm, davri 20 s.
27.7. Amplitudasi 20 sm, tebranish davri 5 s, boshlang’ich fazasi 0 ga teng bo'lgan garmonik tebranish tenglamasini yozing,

A)𝑥 = 0.2 sin 0. 4𝜋𝑡		B)𝑥 = 0.2 sin 5 𝜋𝑡
C) 𝑥 = 20 sin 0. 2𝜋𝑡		𝜋 D)𝑥 = 20 sin (0.4𝜋𝑡 + ) 4 Yechilishi: Berilgan kattaliklarni garmonik harakat tenglamasiga
		qo'yamiz:

𝑥 = 𝑥_𝑚 sin(𝜔𝑡 + 𝜑₀) ;
2𝜋 2𝜋
𝜔 = = = 0.4𝜋
𝑇 5
O'miga go'ysak, quyidagini olamiz.
𝑥 = 0.2 sin( ) 0.4𝜋𝑡