A simple spring – mass vibrating system has a natural frequency of ‘ω_n’. If the spring stiffness is halved and the mass is doubled, then the natural frequency will become

Concept: Consider a spring-mass system

Natural frequency for a spring mass system is

\({\omega _n} = \sqrt {\frac{k}{m}} \)

Calculation:

If stiffness is halved and mass is doubled then

Given: k₂ = k₁/2, m₂ = 2m₁

\({\left( {{\omega _{n2}}} \right)} = \sqrt {\frac{k_2}{{m_2}}} = \sqrt {\frac{k}{{2 \times 2m}}} = \frac{1}{2}\sqrt {\frac{k}{m}} = \frac{1}{2}{\omega _n}\)

∴ the natural frequency will become ω_n / 2