Question

The natural frequency of the system shown below is

• A. $\sqrt{\frac{k}{2m}}$
• B. $\sqrt{\frac{k}{m}}$
• C. $\sqrt{\frac{2k}{m}}$
• D. $\sqrt{\frac{3k}{m}}$

Answer 1

The correct option is A $\sqrt{\frac{k}{2m}}$

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

$\therefore$ $k_{eq}=k/2$

Now natural frequency
$=\sqrt{\frac{k_{eq}}{m}}=\sqrt{\frac{k}{2m}}$