e423b1…: “After the loud raft”

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A modified Hooke’s Law states that the force required to displace a spring $x$ meters from equilibrium is given by $F(x) = kx^2$, where $k$ is a constant of proportionality.

Let $W_1$ denote the work required to stretch the spring $2 m$ from its equilibrium position and $W_2$ denote the work required to stretch the spring $4 m$ from its equilibrium position. Then which of the following describes the relationship between $W_1$ and $W_2$?

$W_2=W_1$ $W_2 = 2 W_1$ $W_2 = 4 W_1$ None of these

In fact, $W_2 = \answer {8} W_1$.