Question

A simple mass-spring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t$, the equation of motion of the free vibration of the system is $m\ddot{z}+kz=0$. The natural frequency of the system is

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

Answer 1

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

For simple harmonic motion
$m\ddot{z}+kz=0$
$\ddot{z}+\frac{k}{m}=0$

Standard equation:
$\frac{d^{2}x}{d{t}^2}+w^{2}x=0$
$\Rightarrow w^2=\frac{k}{m}$
$\Rightarrow w=\sqrt{\frac{k}{m}}$