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Two springs are connected in series and the spring constant determined. If the same two springs...

Two springs are connected in series and the spring constant determined. If the same two springs are connected in parallel, why would the spring constant be different?
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Answer #1

When two springs are connected in series a constant force is applied on one of the springs and total extension is sum of elongation of each spring When two springs are in series F = k1x1 and F = k2x2 so

x1+x2 = total deformation = F/k1 + F/k2 = F/k

k = (1/k1 +1/k2)^-1

When two springs are connected in parallel a constant force F is exerted on both of them and both spring are extended by same amount. System of two parallel spring will equal to single hookean spring

k = k1 + k2

Hence spring constant is different in case of parallel

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