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The equation of motion for a spring-mass system excited by a harmonic force is M x¨ + K x = F cos(ωt), 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. √(M / K)
2. (1 / 2π) √(K / M)
3. 2π √(K / M)
4. √(K / M)

Correct answer: √(K / M)

Solution

The correct option, √(K / M), represents the natural frequency of the spring-mass system, which is the frequency at which the system oscillates when not subjected to external forces. Resonance occurs when the frequency of the external harmonic force matches this natural frequency, leading to maximum amplitude of oscillation.

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