Sum

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?

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#### 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.

Concept: Newton’s Second Law of Motion

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