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Phương trình li độ dao động điều hòa

Lí thuyết Ví dụ minh họa Bài tập vận dụng
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PHƯƠNG TRÌNH LI ĐỘ DAO ĐỘNG ĐIỀU HÒA

1. Lí thuyết

- Phương trình li độ của vật dao động điều hòa có dạng\(x = A\cos (\omega t + {\varphi _0})\)Trong đó: x, A lần lượt là li độ và biên độ dao động của vật, đơn vị là mω là tần số góc của dao động, đơn vị rad/s

φ= ωt+φ0 là pha dao động tại thời điểm t, đơn vị rad

φ0 là pha ban đầu của dao động, đơn vị rad

2. Ví dụ minh họa

Một vật dao động có đồ thị li độ – thời gian được mô tả trong Hình 2.2. Hãy xác định:

a) Biên độ dao động, chu kì, tần số, tần số góc của dao động.
b) Li độ của vật dao động tại các thời điểm t1, t2, t3 ứng với các điểm A, B, C trên đường đồ thị li độ – thời gian.
⛄ c) Độ dịch chuyển so với vị trí ban đầu tại thời điểm t1, t2, t3 trên đường đồ thị.

Phương pháp giải:🅷 Áp dụng kiến thức đã học, sử dụng công thức tính các đại lượng đặc trưng của dao động thông qua đồ thị

Lời giải chi tiết:

a) Biên độ dao động A=0,2 cmChu kì T=0,4 s

Tần số \(f = \frac{1}{T} = \frac{1}{{0,4}} = 2,5Hz\)
ไ Tần số góc của dao động \(\omega  = \frac{{2\pi }}{T} = \frac{{2\pi }}{{0,4}} = 5\pi rad/s\)

b) Li độ của vật dao động tại các thời điểm t1, t2, t3 ứng với các điểm A, B, C trên đường đồ thị li độ – thời gian lần lượt là x1=-0,1 cm, x2= -0,2 cm, x3= 0 cm.

c) Vì gốc thời gian trùng với vị trí cân bằng nên li độ cũng chính là độ dịch chuyển từ vị trí cân bằng đến vị trí của vật tại các điểm A, B, C.Biên độ trong dao động điều hòa

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