Question
Derive the expression for resultant spring constant when two springs having constants k1 and k2 are connected
- In parallel.
- In series.
✓
Answer
- When the springs are connected in parallel, the extension in them will be same and the total restoring force is the sum of their restoring forces.
$\therefore\text{F = F}_1+\text{F}_2$
$-\text{k}_{\text{eq}}\text{x}=-\text{k}_1\text{x}-\text{k}_2\text{x}$
$\text{k}_{\text{eq}}=\text{k}_1+\text{k}_2$
- When the springs are connected in series, the restoring force is same in both the springs and the extensions will be different so the not extension
i.e., $\text{x = x}_1+\text{x}_2$
$=\frac{\text{F}}{-\text{k}_{\text{eq}}}=\frac{-\text{F}}{\text{k}_1}-\frac{\text{F}}{\text{k}_2}$
$\therefore\frac{1}{\text{k}_{\text{eq}}}=\frac{1}{\text{k}_1}+\frac{1}{\text{k}_2}$
when connected in series.
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