Question

What is the spring constant in parallel connection and series connection?

Answer 1

Spring constant in parallel connection:

1. Whenever two massless springs that obey Hooke's Law are joined by a thin, vertical rod, they are linked in parallel. The spring constants for springs $1$ and $2$ were indeed denoted by ${\text{k}}_1$ and ${\mathrm{k}}_2$. A steady force F is applied to the rod, keeping it perpendicular to the force's orientation. If the force was reciprocated, the springs may likewise be squeezed.
2. Such a system of two parallel springs is equal to a single Hookean spring with spring constant k. To calculate the value of k, use the following formula.

Mathematical representation:

${\mathrm{k}}_{\mathrm{p}}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3...$

Spring constant in series connection:

1. The springs are extended throughout this connection, and the overall extension of the arrangement corresponds to the summation of each spring's elongation. Conversely, by reversing the force orientation, the springs might be compressed.
2. This configuration of two springs in series is equal to a single spring with spring constant k. To compute the value of k, use the following formula.

Mathematical representation:

$\frac{1}{{\mathrm{k}}_{\mathrm{s}}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}...$