11. [1 mark] The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension $x$ is $E$. What is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$ ?

Step 1 ：Given the energy stored in the spring at extension $x$ is $E$, we can use the formula for the potential energy stored in a spring: $PE = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the extension.

Step 2 ：Find the spring constant $k$ by solving for $k$ in the equation $E = \frac{1}{2}kx^2$. We get $k = \frac{2E}{x^2}$.

Step 3 ：Find the energy stored in the spring at extension $\frac{x}{4}$ using the formula $PE = \frac{1}{2}k(\frac{x}{4})^2$. Substitute the value of $k$ we found earlier: $PE = \frac{1}{2}(\frac{2E}{x^2})(\frac{x}{4})^2$. This simplifies to $PE = 0.0625E$.

Step 4 ：Find the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$ by finding the difference between the two energies: $Work = E - 0.0625E$. This simplifies to $Work = 0.9375E$.

Step 5 ：\(\boxed{0.9375E}\) is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$.