We can make a static measurement to deduce the spring constant to use in the model. If a \(61 \mathrm{~kg}\) woman stands on a low wall with her full weight on the ball of one foot and the heel free to move, the stretch of the Achilles tendon will cause her center of gravity to lower by about \(2.5 \mathrm{~mm}\). What is the spring constant?

A. \(1.2 \times 10^{4} \mathrm{~N} / \mathrm{m}\)

B. \(2.4 \times 10^{4} \mathrm{~N} / \mathrm{m}\)

C. \(1.2 \times 10^{5} \mathrm{~N} / \mathrm{m}\)

D. \(2.4 \times 10^{5} \mathrm{~N} / \mathrm{m}\)

We saw that a runner's Achilles tendon will stretch like a spring and then rebound, storing and returning energy during a step. We can model this as the simple harmonic motion of a mass-spring system. When the foot rolls forward, the tendon spring begins to stretch as the weight moves to the ball of the foot, transforming kinetic energy into elastic potential energy. This is the first phase of an oscillation. The spring then rebounds, converting potential energy to kinetic energy as the foot lifts off the ground. The oscillation is fast: Sprinters running a short race keep each foot in contact with the ground for about 0.10 second, and some of that time corresponds to the heel strike and subsequent rolling forward of the foot.