Question

Find the effective spring constant of the parallel-spring system shown in Figure 5.1.5when both springs have the spring constant. Give a physical interpretation of this result.

Short answer

$K_{effective}=2K$

Step-by-step solution

Definition:

Spring Constant or force constant is defined as the applied force if the displacement in the spring is unity.

Interpretation:

Two springs have the same spring constant.

$k_1=k_2=k$

Effective spring constant of the parallel-spring system is

$\begin{array}{rcl}{k}_3& =& k_1+k_2\\ & =& k+k\\ & =& 2k\end{array}$

Physical interpretation of the result:

Suppose two parallel springs with same spring constants are attached to a common rigid support and then to a single mass $m$, then the effective spring constant of the parallel spring system equals twice the spring constant of each spring.