Answer
See work.
Work Step by Step
Though the astronaut is apparently weightless, she still has inertia. If the astronaut is attached to a stiff spring and oscillates back and forth, the frequency of oscillation depends on the mass (as later seen in Equations 14.10-14.12). The larger the mass, the slower the oscillations. The period for one complete cycle is $T=2\pi\sqrt{\frac{m}{k}}$, where k is the stiffness (“spring constant”) of the spring.
