If $K_i$ and $K_p$ respectively are effective spring constant in series and parallel combination of springs as shown in figure, find $\displaystyle\frac{K_i}{K_p}$

Question

Accepted Answer

In a series combination of above springs, effective spring constant  $K_i=\dfrac{K_1 K_2}{K_1+K_2}$ $\therefore$  $K_i=\dfrac{K\times 2K}{K+2K}$ $=\dfrac{2K}{3}$In parallel combination of above springs, effective spring constant  $K_p=K_1+K_2$$\therefore$  $K_p = K+2K = 3K$Thus $\dfrac{K_i}{K_p}=\dfrac{2K/3}{3K}=\dfrac{2}{9}$

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If $K_{i}$ and $K_{p}$ respectively are effective spring constant in series and parallel combination of springs as shown in figure, find $\frac{K _{i}}{K _{p}}$