Đáp án:
a) \(\dfrac{{2\sqrt 5 }}{5}\left( s \right)\)
b) \(25N/m\) ; \(\dfrac{{2\pi }}{5}\left( s \right)\)
\(100N/m\) ; \(\dfrac{\pi }{5}\left( s \right)\)
Giải thích các bước giải:
a) Chu kỳ là:
\(T = \dfrac{{2\pi }}{\omega } = 2\pi \sqrt {\dfrac{m}{k}} = 2\pi \sqrt {\dfrac{1}{{50}}} = \dfrac{{2\sqrt 5 }}{5}\left( s \right)\)
b)
* Ghép nối tiếp:
\(\begin{array}{l}
k' = \dfrac{{{k_1}{k_2}}}{{{k_1} + {k_2}}} = \dfrac{k}{2} = 25N/m\\
\Rightarrow T' = 2\pi \sqrt {\dfrac{m}{{k'}}} = 2\pi \sqrt {\dfrac{1}{{25}}} = \dfrac{{2\pi }}{5}\left( s \right)
\end{array}\)
* Ghép song song:
\(\begin{array}{l}
k' = {k_1} + {k_2} = 2k = 100N/m\\
\Rightarrow T' = 2\pi \sqrt {\dfrac{m}{{k'}}} = 2\pi \sqrt {\dfrac{1}{{100}}} = \dfrac{\pi }{5}\left( s \right)
\end{array}\)