\(a)\\\) Pha ban đầu: \(\begin{cases}\varphi_x=\varphi_a-\pi=\dfrac{\pi}{3}-\pi=-\dfrac{2\pi}{3}(rad)\\\varphi_v=\varphi_a-\dfrac{\pi}{2}=\dfrac{\pi}{3}-\dfrac{\pi}{2}=-\dfrac{\pi}{6}(rad)\end{cases}\)

Biên độ : \(A\omega^2=20\Rightarrow A=\dfrac{20}{\omega^2}=\dfrac{20}{\pi^2}\approx 2(cm)\)

Vận tốc cực đại: \(v_{max}=A\omega =2\pi(cm/s)\)

Phương trình li độ:

\(x=A\cos\left(\omega t+\varphi_x\right)\\\Rightarrow x=2\cos\left(\pi t-\dfrac{2\pi}{3}\right)\)

Phương trình vận tốc:

\(x=v_{max}\cos\left(\omega t+\varphi_v\right)\\\Rightarrow v=2\pi\cos\left(\pi t-\dfrac{\pi}{6}\right)\)

\(b)\\t=2023(s)\Rightarrow \begin{cases} x=2\cos\left(\pi .2023-\dfrac{2\pi}{3}\right)=1(cm)\\v=2\pi\cos\left(\pi.2023-\dfrac{\pi}{6}\right)=-\pi\sqrt{3}(cm/s)\end{cases}\\c)\\a=-10(cm/s^2)=-\omega^2x\Rightarrow x=-\dfrac{10}{\omega^2}\approx -1(cm)\\\Rightarrow W_d=W-W_t\\=\dfrac{1}{2}m\omega^2A^2-\dfrac{1}{2}m\omega^2x^2\\=\dfrac{1}{2}.0,5\pi^2.0,02^2-\dfrac{1}{2}.0,5.\pi^2.(-0,01)^2\\=7,5.10^{-4}(J)\)