Physics - NLM Question with Solution | TestHub

The total restoring force is related to extension as follows: $f=-Kx---(1)$ The extension in the springs are related to the restoring force as follows: $f=-K_1{e}_1---(2)$ and $f=-K_2{e}_2---(3)$ The total extension of the springs is: $x=e_1+e_2---(4)$ Using equation (1),(2) and (3) $\begin{array}{rl}& \Rightarrow \left(-\frac{f}{K}\right)=\left(-\frac{f}{K_1}\right)+\left(-\frac{f}{K_2}\right)\\ & \Rightarrow \frac{1}{K}=\left(\frac{1}{K_1}+\frac{1}{K_2}\right)---(5)\end{array}$ The total extension using equation (4) and (5)is given by, $x=\frac{f}{K}=f\left(\frac{1}{K_1}+\frac{1}{K_2}\right)$