Question

What is the equivalent spring constant for the system shown below?

• A. $\frac{2k}{3}$
• B. $\frac{k}{3}$
• C. $\frac{4k}{3}$
• D. $\frac{3k}{2}$

Answer 1

The correct option is C $\frac{4k}{3}$

As in the given arrangement two springs in either side of the block are in series, thus equivalent spring constant for either side is given as
$k^{{}^{\prime }}=\frac{k\times 2k}{k+2k}=\frac{2k}{3}$
And, these two equivalents are in parallel together, hence, the equivalent spring constant for entire system is given as
$k_{eq}=k^{{}^{\prime }}+k^{{}^{\prime }}=\frac{2k}{3}+\frac{2k}{3}=\frac{4k}{3}$