Question
Explain force displacement graph for a spring.
✓
Answer
Since the restoring spring force and displacement are linearly related as $F=-k x$, and are opposite in direction, the graph between $F$ and $x$ is a straight line with dwelling only in the second and fourth quadrant as shown in Figure. The elastic potential energy can be easily calculated by drawing a $F - x$ graph. The shaded area (triangle) is the work done by the spring force.
$
\text { Area }=\frac{1}{2}(\text { base })(\text { height })=\frac{1}{2} \times(x) \times(k x)=\frac{1}{2} k x^2
$
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