Two springs of spring constants $$k1$$ and $$k2$$ are joined in series. The effective spring constant of $$the-combination$$ is given by:

Question

Two springs of spring constants $$k1$$ and $$k2$$ are joined in series. The effective spring constant of $$the-combination$$ is given by:

Infinity Learn · Accepted Answer

Let us consider two springs of spring constants $$k1$$ and $$k2$$ joined in series as shown in the figure.Under a force F, they will stretch by $$y1$$ and $$y2$$.So y $$=$$ $$y1+y2or$$ Fk  $$=$$ $$F1k1+F2k2but$$ as springs are massless, so force on them must be the same, i,e., $$F1$$ $$=$$ $$F2$$ $$=$$ FSo, $$1k$$ $$=$$ $$1k1+1k2$$     or  k $$=$$ $$k1k2k1+k2Aliter$$: In series combination,$$1kS$$ $$=$$ $$1k1+1k2$$ $$=$$ $$k2+k1k1k2$$     ⇒kS $$=$$ $$k1k2k1+k2$$

Two springs of spring constants $k_{1} and k_{2}$ are joined in series. The effective spring constant of the-combination is given by:

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Two springs of spring constants k1 and k2 are joined in series. The effective spring constant of the-combination is given by:

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Two springs of spring constants $k_{1} and k_{2}$ are joined in series. The effective spring constant of the-combination is given by: