Question

The natural frequencies corresponding to the spring-mass systems I and II are ${\omega }_I$ and ${\omega }_{II}$, respectively. The ratio $\frac{{\omega }_I}{{\omega }_{II}}$ is

• A. 2
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. 4

Answer 1

The correct option is B $\frac{1}{2}$

$\frac{1}{k_{eq}}=\frac{1}{k}+\frac{1}{k}=\frac{2}{k}$



$k_{eq}=\frac{k}{2}$

$\Rightarrow {\omega }_1=\sqrt{\frac{\left(k/2\right)}{m}}=\sqrt{\frac{k}{2m}}$


${\omega }_2=\sqrt{\frac{2k}{m}}$

$\frac{{\omega }_1}{{\omega }_2}=\sqrt{\frac{k/2m}{2k/m}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

$\frac{{\omega }_1}{{\omega }_2}=\frac{1}{2}$