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The equation of motion for a spring-mass system excited by a harmonic force is

\(M\ddot x + kx = F\cos \left( {\omega t} \right),\)

Where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to
1. \(\sqrt {\frac{M}{k}}\)
2. \(\frac{1}{{2\pi }}\sqrt {\frac{k}{M}}\)
3. \(2\pi \sqrt {\frac{k}{M}}\)
4. \(\sqrt {\frac{k}{M}}\)

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Correct Answer - Option 4 : \(\sqrt {\frac{k}{M}}\)

Concept:

When the natural frequency of the system coincides with the external forcing frequency, it is called resonance, that is, ω = ωn

The natural frequency of a given spring-mass system is:

\(M\ddot x + kx = F\cos \left( {\omega t} \right)\)

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

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