Question

1) Cho cac phuong trinh dao dong sau:

a) x₈ = 2sin 4πt + 2cos 4πt (cm)

b) x₇ = 3sin ( -5t - \(\dfrac{\Pi}{6}\)) (cm)

c) x₄ = 5cos 2πt + 3 (mm)

Xac dinh bien do, pha ban dau, chu ky cua moi dao dong

Answer 1

\(x=Acos\left(\omega t+\varphi_0\right)\)

a)\(x_8=2sin4\pi t+2cos4\pi t=2\left(sin4\pi t+cos4\pi t\right)=2\cdot\sqrt{2}cos\left(4\pi t-\dfrac{\pi}{4}\right)\)

Biên độ: \(A_1=2\sqrt{2}cm\)

Pha ban đầu: \(\varphi_0=-\dfrac{\pi}{4}\)

Chu kì: \(T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}s\)

b)\(x_7=3sin\left(-5t-\dfrac{\pi}{6}\right)=3cos\left(5t+\dfrac{\pi}{6}+\dfrac{\pi}{2}\right)=3cos\left(5t+\dfrac{2\pi}{3}\right)\)

Biên độ: \(A=3cm\)

Pha ban đầu: \(\varphi_0=\dfrac{2\pi}{3}\)

Chu kì: \(T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{5}s\)

c)\(x_4=5cos\left(2\pi t+3\right)mm\)

\(A=5mm;\varphi_0=3rad;T=\dfrac{2\pi}{\omega}=1s\)