Question

A mass m is attached to two identical springs having constant k as shown in the figure. The natural frequency $\omega$ of this single degree of freedom system is

• A. $\sqrt{\frac{2k}{m}}$
• B. $\sqrt{\frac{k}{m}}$
• C. $\sqrt{\frac{k}{2m}}$
• D. $\sqrt{\frac{4k}{m}}$

Answer 1

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

Equivalent stiffness,
$k_{eq}=k+k=2k$

Natural frequency,

${\omega }_n=\sqrt{\frac{k_{eq}}{m}}=\sqrt{\frac{2k}{m}}$