What is the natural frequency of the system shown if k₁ = k₂ = k₃ = 10 lb/ft?

Spring Forces

Stiffness constant of two springs in parallel,
     F₁ + F₂ = F
     x k₁ + x k₂ = x k₁₂
     k₁ + k₂ = k₁₂

Stiffness constant of two springs in series,
     x₁ + x₂ = x
     F/k₁ + F/k₂ = F/k₁₂
     1/k₁ + 1/k₂ = 1/k₁₂

For the current spring configuration, combine k₁ and k₂ (series) first,
     1/k₁₂ = 1/k₁ + 1/k₂
             = 1/10 + 1/10
     k₁₂ = 5

The combined k₁₂ and k₃ (parallel),
     k₁₂₂ = k₁₂ + k₃
            = 5 + 10 =15

The natural frequency of the combined system is,
     ω = (k₁₂₂/m)^0.5 = (15/2)^0.5

ω = 2.739 rad/s