A spring which is initially in its natural length, first stretched by a length x and then again by a further length x . The work done in the first case is W and in the second case W 1 . Then,

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Since, we know, work done in stretching a spring from $x_{1}$ to $x_{2}$ is

$W = \frac{1}{2} k (x_{2}^{2} - x_{1}^{2})$

In $1^{s t}$ case, $W = \frac{1}{2} k (x^{2} - 0) = \frac{1}{2} k x^{2}$ .... (i)

In $2^{n d}$ case, $W_{1} = \frac{1}{2} k [{(2 x)}^{2} - x^{2}] = \frac{1}{2} k [4 x^{2} - x^{2}]$

$= \frac{1}{2} k . 3 x^{2} = 3 . \frac{1}{2} k x^{2}$

$= 3 W$ [From Eq. (i)]

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