Both the springs shown in 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 $m$ towards left through displacement $x$ .
$F_{1} = k_{1} \times$ (compressed)
$F_{2} = k_{2} \times$ (expanded)
They are in same direction.
Resultant $F = F_{1} + F_{2} \Rightarrow F = k_{1} x + k_{2} x \Rightarrow F = x (k_{1} + k_{2})$
So, a = acceleration $= \frac{F}{m} = \frac{x (k_{1} + k_{2})}{m}$ opposite to the displacement.

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Both the springs shown in figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?

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