题目
有两根倔强系数同为 k 弹簧并联在一起，一端固定，在另一端挂一质量为 m 的重物，使其构成一竖挂的弹簧谐振子，则此系统的振动周期为____Two stubbornness coefficients k are the same. The springs are connected in parallel. If one end is fixed and a weight of mass is hung on the other end to form a vertical spring resonator, the vibration period of the system is____A. 2pisqrt((m)/(k))B. 2pisqrt((2m)/(k))C. 2pisqrt((m)/(2k))D. pisqrt((m)/(k))
有两根倔强系数同为 $k$ 弹簧并联在一起，一端固定，在另一端挂一质量为 $m$ 的重物，使其构成一竖挂的弹簧谐振子，则此系统的振动周期为____
Two stubbornness coefficients $k$ are the same. The springs are connected in parallel. If one end is fixed and a weight of mass is hung on the other end to form a vertical spring resonator, the vibration period of the system is____
A. $2\pi\sqrt{\frac{m}{k}}$
B. $2\pi\sqrt{\frac{2m}{k}}$
C. $2\pi\sqrt{\frac{m}{2k}}$
D. $\pi\sqrt{\frac{m}{k}}$
题目解答
答案
两根倔强系数均为 $ k $ 的弹簧并联，等效劲度系数为 $ k_{\text{总}} = 2k $。根据弹簧振子周期公式：
\[
T = 2\pi \sqrt{\frac{m}{k_{\text{总}}}} = 2\pi \sqrt{\frac{m}{2k}}
\]
竖直悬挂时，重力仅影响静止位置，不影响振动周期。因此，系统的振动周期为 $ T = 2\pi \sqrt{\frac{m}{2k}} $。
答案：C. $ 2\pi\sqrt{\frac{m}{2k}} $