Question

If $k_{s}$ and $k_{p}$ respectively are effective spring constant in series and parallel combination of springs as shown in the figure, find $\frac{ k _{ s ⁡}}{ k ⁡_{ p ⁡}}$

• A. $\frac{9}{2}$
• B. $\frac{3}{7}$
• C. $\frac{2}{9}$
• D. $\frac{7}{3}$

Answer 1

Answer: (C)

The effective spring constant $k_{s}$ of this arrangement is
$\frac{1}{k_{s}}=\frac{1}{k}+\frac{1}{2 k} $
$\frac{1}{k_{s}}=\frac{2+1}{2 k}=\frac{3}{2 k}$
$k_{s}=\frac{2 k}{3}$
The effective spring constant $k_{p}$ of this arrangement is
$k_{p}=k_{1}+k_{2}$
$=k+2 k=3 k$
$\therefore \frac{k_{s}}{k_{p}}=\frac{2 k / 3}{3 k}=\frac{2}{9}$