一质量为$m$的刚体，在重力矩的作用下绕固定的水平轴O作小幅度无阻尼自由摆动(如图所示)。设刚体质心C支轴线O的距离为b，刚体对轴线O的转动惯量为$I$。该体系的振动周期是
A: $T=2\pi\sqrt{I/(2mgb)}$
B: $T=2\pi\sqrt{2I/(mgb)}$
C: $T=2\pi\sqrt{I/(mgb)}$
D: 上述答案都不正确
A: $T=2\pi\sqrt{I/(2mgb)}$
B: $T=2\pi\sqrt{2I/(mgb)}$
C: $T=2\pi\sqrt{I/(mgb)}$
D: 上述答案都不正确
举一反三
- \(\int_{-\sqrt{2}}^{\sqrt{2}}{\sqrt{8-2 { { y}^{2}}}dy}\)=( )。 A: \(\sqrt{2}(\pi -2)\) B: \(\sqrt{2}(\pi +2)\) C: \(2\sqrt{2}(\pi +2)\) D: \(2\sqrt{2}(\pi -2)\)
- 1.7 一长为\(l\)的均匀细棒悬于通过其一端的光滑水平轴上．作成一复摆．已知细棒绕通过其一端的轴的转动惯量\(J=ml^2/3\)，此摆作微小振动的周期为 A: 2\(\pi\)\(\sqrt{\frac{l}{g}}\) B: 2\(\pi\)\(\sqrt{\frac{l}{2g}}\) C: 2\(\pi\)\(\sqrt{\frac{2l}{3g}}\) D: \(\pi\)\(\sqrt{\frac{l}{3g}}\)
- $\int_{0}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{4}}{[\cos (2t)\mathbf{i}+\sin (2t)\mathbf{j}+t\sin t\mathbf{k}]}\operatorname{dt}=$( ) A: $(\frac{1}{2},\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ B: $(1,\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ C: $(\frac{1}{2},1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ D: $(1,1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$
- 下列MATLAB命令中表示复数1+i的为______ A: 2^(1/2)*exp(pi/4*i) B: sqrt(2)*exp(pi/4*i) C: 1+i D: 1+sqrt(-1)
- 曲线$\left\{ \matrix{ {x^2} + {y^2} + {z^2} = 9 \cr y = x \cr} \right.$的参数方程为( ). A: $$\left\{ \matrix{ x = \sqrt 3 \cos t \cr y = \sqrt 3 \cos t \cr z = \sqrt 3 \sin t \cr} \right.(0 \le t \le 2\pi )$$ B: $$\left\{ \matrix{ x = {3 \over {\sqrt 2 }}\cos t\cr y = {3 \over {\sqrt 2 }}\cos t \cr z = 3\sin t \cr} \right.(0 \le t \le 2\pi )$$ C: $$\left\{ \matrix{ x = \cos t\cr y = \cos t\cr z = \sin t \cr} \right.(0 \le t \le 2\pi )$$ D: $$\left\{ \matrix{ x = {{\sqrt 3 } \over 3}\cos t\cr y = {{\sqrt 3 } \over 3}\cos t \cr z = {{\sqrt 3 } \over 3}\sin t\cr} \right.(0 \le t \le 2\pi )$$