Question:
Natural frequency of undamped SDOF system is:
Natural frequency of undamped SDOF system is:
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In an SDOF spring-mass system, natural frequency $\omega_n = \sqrt{k/m}$; it's the square root of stiffness over mass.
Updated On: Jun 21, 2025
- $\sqrt{\frac{m}{k}}$
- $\sqrt{\frac{k}{m}}$
- $\frac{k}{m}$
- $\frac{m}{k}$
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The Correct Option is B
Solution and Explanation
An undamped Single Degree of Freedom (SDOF) system follows the differential equation:
\[
m \ddot{x} + kx = 0
\]
The general solution to this equation represents harmonic motion with angular natural frequency $\omega_n$ given by:
\[ \omega_n = \sqrt{\frac{k}{m}} \]
Where: $k$ = stiffness of the spring (N/m)
$m$ = mass of the system (kg)
Thus, the natural frequency of vibration (in rad/s) is $\omega_n = \sqrt{k/m}$.
The general solution to this equation represents harmonic motion with angular natural frequency $\omega_n$ given by:
\[ \omega_n = \sqrt{\frac{k}{m}} \]
Where: $k$ = stiffness of the spring (N/m)
$m$ = mass of the system (kg)
Thus, the natural frequency of vibration (in rad/s) is $\omega_n = \sqrt{k/m}$.
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