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
$\frac{1}{k_s}=\frac{1}{k}+\frac{1}{2k}$
$\frac{1}{k_s}=\frac{2+1}{2k}=\frac{3}{2k}$
$k_s=\frac{2k}{3}$
The effective spring constant $k_p$ of this arrangement is
$k_p=k_1+k_2$
$=k+2k=3k$
$\therefore \frac{k_s}{k_p}=\frac{2k/3}{3k}=\frac{2}{9}$