Springs in Series and Parallel (Series: 1/k_eff = 1/k₁ + 1/k₂. Parallel: k_eff = k₁ + k₂)

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Series: 1/k_eff = 1/k₁ + 1/k₂. Parallel: k_eff = k₁ + k₂

What each symbol means

SymbolWhat it stands for
k_effEffective spring constant of combination (N/m)
k₁, k₂Individual spring constants (N/m)

When to use this

Series: same force, extensions add → softer (k_eff < min(k₁,k₂)). Parallel: same extension, forces add → stiffer (k_eff > max(k₁,k₂)). Two springs on either side of a block = parallel combination. Cutting a spring of constant k into n equal parts gives each part constant nk.