\(v_{max}=20\pi\)cm/s\(=0,2\pi m\)/s
\(g_{max}=a_{max}=8m\)/s2
Mà \(\dfrac{v_{max}}{g_{max}}=\dfrac{\omega A}{\omega^2A}=\dfrac{1}{\omega}=\dfrac{T}{2\pi}\Rightarrow\dfrac{0,2\pi}{8}=\dfrac{T}{2\pi}\)
\(\Rightarrow T=0,2\pi\cdot2\pi\cdot8=32s\)\(\Rightarrow\omega=\dfrac{2\pi}{T}=\dfrac{\pi}{16}\) (rad/s)
Mặt khác: \(\omega=\sqrt{\dfrac{k}{m}}\Rightarrow k=\omega^2\cdot m=\left(\dfrac{\pi}{16}\right)^2\cdot0,5=\dfrac{10}{16^2}\cdot0,5=0,02\)N/m