Both the springs shown in figure $(5 - E 2)$ are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?

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Solution

Given that,

Spring constant $= k$

Displacement $= x$

Let x be the initial displacement of the block. Then the force on the block are $- k_{1} x$ and $- k_{2} x$

So, the force is

$F = - k_{1} x - k_{2} x$

$F = - (k_{1} x + k_{2} x)$

Now, the acceleration is

$F = m a$

$a = \frac{F}{m}$

$a = \frac{- (k_{1} + k_{2}) x}{m}$

Hence, the acceleration is $\frac{- (k_{1} + k_{2}) x}{m}$

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