2014: Problem 11

Topic: Energy
Concepts: Conservation of energy, Kinetic energy, Spring potential energy

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Solution:

By conservation of energy, we have

$$E=K+U$$

$$K(U)=-U+E$$

which is a line with slope $-1$ and intercept $E$.

Since $K=\frac{1}{2}mv^2 \geq 0$ and $U=\frac{1}{2}kx^2 \geq 0$, the plot only exists in the first quadrant. Thus, the answer is E.

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