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?

Answer 1

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.