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

Javob: A) 𝑥 = 0.2 sin( ) 0.4𝜋𝑡
27.8. Garmonik tebranishlar amplitudasi 1 m, boshlang’ich fazasi n, tebranishlar davri 2 s bo'Isa, shu tebranish tenglamasi qanday bo'ladi?
A)𝑥 = cos(2𝜔𝑡 + 𝜋) B)𝑥 = cos(2𝑡 + 𝜋)
C)𝑥 = 𝐴 cos(2𝜋𝑡 + 𝜋) D)𝑥 = cos(𝜋𝑡 + 𝜋)
Yechilishi: Berilgan kattaliklami garmonik harakat tenglamasiga go'yamiz.
𝑥 = 𝑥_𝑚 cos(𝜔𝑡 + 𝜑₀)
2𝜋 2𝜋

𝜔 = = = 𝜋 𝑇 2
O'riga qo'ysak, quyidagini olamiz:
𝑥 = cos(𝜋𝑡 + 𝜋)
Javob: D) 𝑥 = cos(𝜋𝑡 + 𝜋)
𝜋
27.9. Amplitudasi 1 mm, chastotasi 1000 Hz boshlang’ich fazasi bo’lgan garmonik tebranishlarning 3
tenglamasini tuzing.
𝜋 𝜋
A)𝑥 = 0.001 cos (2000𝜋𝑡 + ) B)𝑥 = sin (1000𝜋𝑡 + )
3 3
𝜋
C)𝑥 = cos (1000𝜋𝑡 + ) D)𝑥 = 0.001 sin(2000𝜋𝑡) 3
Yechilishi: Berilgan kattaliklarni garmonik harakat tenglamasiga qo'yamiz:
𝑥 = 𝑥_𝑚 cos(𝜔𝑡 + 𝜑₀);
𝜔 = 2𝜋𝜈 = 2𝜋 ⋅ 1000 = 2000𝜋
O'miga qo'ysak, quyidagini olamiz:
𝜋
𝑥 = 0.001 cos (2000𝜋𝑡 + ) 3
𝜋
Javob: A) 𝑥 = 0.001 cos (2000𝜋𝑡 + )
3
𝜋
27.10. Garmonik tebranish amplitudasi 3 m, boshlang’ich fazasi , tebranishlar soni minutiga 180 2
bo'lsa, quyidagi ifodalarning qaysi biri shu tebranish tenglamasi bo'ladi?
𝜋
A) 𝑥 = 3 cos (2𝜋𝑡 + 2) B)𝑥 = cos(2𝜋𝑡 + 𝜑₀)
𝜋
C)𝑥 = 3 cos (6𝜋𝑡 + 2) D)𝑥 = cos(cos 2 𝜋𝑡 + 𝜑₀)
Yechilishi: Berilgan kattaliklarni garmonik harakat tenglamasiga qo’yamiz:
𝑥 = cos(𝜔𝑡 + 𝜑₀)
Siklik chastotani topib olamiz:
𝑁
𝜈 = ;
𝑡
2𝜋𝑁 2𝜋 ⋅ 180𝜋
𝜔 𝜋
O'rniga qo'ysak, quyidagini olamiz:
𝜋
𝑥 = 3 cos (6𝜋𝑡 + ) 2
𝜋
Javob: C)𝑥 = 3 cos (6𝜋𝑡 + )
2
27.11. Bikrligi 400 N/m bo'lgan prujinaga osilgan 1 kg massali yuk 12sm amplituda bilan tebranmoqda. Shu tebranishning matematik qonunini ko’sating.

A) 𝑥 = 0.4 cos 1 20𝑡		B)𝑥 = 0.4 cos 1 2𝑡
C) 𝑥 = 0.12 cos 2 0𝑡		D)𝑥 = 0.12 cos 4 0𝑡

Yechilishi:Berilgan Kattaliklarni garmonik harakat tenglamasiga qo'yamiz:

𝑥 = 𝑥_𝑚 cos(𝜔𝑡 + 𝜑₀)
Siklik chastotani prujinaning tebranish davriga bog’lanish
formulasidan:

2𝜋 2𝜋 𝑘 400 20𝑟𝑎𝑑

𝜔 = = √ = √ = 𝑇 𝑡 𝑠
O'rniga qo’ysak quyidagini olamiz:
𝑥 = 0.12 cos 2 0𝑡