Question

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

• A. $5k$
• B. $3.5k$
• C. $1.5k$
• D. $0.5k$

Answer 1

The correct option is B $3.5k$

As in the given arrangement two springs in left side of the block are in parallel and the two in the right side of the block are in series,
Thus equivalent spring constant for left side of the block is given as
$k_{left}=k+2k=3k$
similarly, for right side of the block
$k_{right}=\frac{k\times k}{k+k}=\frac{k}{2}$
And, these two equivalents are in parallel together, hence, the equivalent spring constant for entire system is given as
$k_{eq}=k_{left}+k_{right}=3k+\frac{k}{2}=3.5k$