A runner's Achilles tendon will stretch like a spring and then rebound, storing and returning energy during a step. This can be modelled 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 tendon spring then rebounds, in the second phase of the oscillation, 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 $0\mathrm{.}10$ second, which corresponds to a complete oscillation of heel strike, rolling forward onto the ball of the foot $($stretch$),$ and foot lifting off $($rebound$).$ Assume that the "spring constant" for a runner's Achilles tendon is $2\mathrm{.}39{10}^5\frac{N}{m}$ and that the runner has a mass of $61kg.$

If$,$ during a stride, the stretch causes the runner's center of mass to lower by $10mm,$ what is the stored energy?

a$.3\mathrm{.}0J$

b$.,6\mathrm{.}0J$

c$.9\mathrm{.}0J$

d$.12J$