Question

If two springs k₁ and k₂ are placed in parallel, the combined stiffness of spring is
1. k₁ + k₂
2. k₁ + k₂ / (k₁ k₂)
3. (k₁ k₂) / k₁ + k₂
4. k₁ k₂

Answer 1

Correct Answer - Option 1 : k₁ + k₂

Explanation:

Springs in Series and Parallel:

1. Springs in Series: If springs are in series, then force in each spring will be equal. Then, total extension,

Δ = Δ₁ + Δ₂

⇒ \(\frac{P}{{{K_1}}} + \frac{P}{{{K_2}}} = \frac{P}{{{K_{eq}}}}\)

\(\frac{1}{{{k_{eq}}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}}\)

2. Springs in Parallel: In parallel combination, force developed in each spring will be different but deflection in each spring will be equal.

P = P₁ + P₂

K_eqΔ = K₁Δ + K₂Δ 

K_eq = K₁ + K₂