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(C) The work done in stretching a spring by a length $x$ from its natural length is given by $W = \frac{1}{2}Kx^2$, where $K$ is the spring constant.F

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$3W_1$

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(C) The work done in stretching a spring by a length $x$ from its natural length is given by $W = \frac{1}{2}Kx^2$, where $K$ is the spring constant.For the first step, the extension is $x$, so the work done is $W_1 = \frac{1}{2}Kx^2$.For the second step, the spring is stretched from an extension of $x$ to an extension of $2x$. The work done $W_2$ is the change in potential energy:$W_2 = U_{final} - U_{initial} = \frac{1}{2}K(2x)^2 - \frac{1}{2}Kx^2$.$W_2 = \frac{1}{2}K(4x^2) - \frac{1}{2}Kx^2 = \frac{1}{2}K(3x^2) = 3(\frac{1}{2}Kx^2)$.Since $W_1 = \frac{1}{2}Kx^2$, we have $W_2 = 3W_1$.

The spring is initially in an unstretched condition. It is first stretched by a length $x$ and the work done is $W_1$. Then again it is stretched by a further length $x$ such that the total extension becomes $2x$. The work done in this second step is $W_2$. The value of $W_2$ is given by

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