Question

What is the equivalent spring constant for the syatem shown below in the figure?
(All the springs are ideal and identical having spring constant $k\text{N/m}$)

• A. $\frac{6k}{7}$
• B. $\frac{3k}{5}$
• C. $\frac{2k}{5}$
• D. $2k$

Answer 1

The correct option is C $\frac{2k}{5}$

Given system is as shown below

From the arrangement we can see that, $C$ and $D$ are together in series, also $A$ and $B$ are together in parallel.
So, we have
$K_{CD}=\frac{k\times k}{k+k}=\frac{k}{2}$
Also, $K_{AB}=k+k=2k$
Now, these two equavalents are in series, so the final eqivalent spring constant is given as
$K_{eq}=\frac{\frac{k}{2}\times 2k}{\frac{k}{2}+2k}=\frac{2k}{5}$