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Question
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
Solution
Let the block m be displaced towards left by displacement x.
\[\therefore F_1 = -K_1X\] (compressed)
\[ F_2 = -K_2X\] (expanded)
\[ma = F_1 + F_2\]
\[\Rightarrow a = \frac{- x\left( k_1 + k_2 \right)}{m}\]
i.e. \[\left( k_1 + k_2 \right)\frac{x}{m}\] opposite the displacement or towards the mean position.
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