Essential University Physics: Volume 1 (3rd Edition)

$$k = 39 N/m$$
We know: $$\omega = \frac{a}{v}=10.6 Hz$$ For part b, we know that: $$A = \frac{v_{max}}{ \omega} = .17 m$$ Lastly, solving for the spring constant gives: $$F = kA$$ $$\frac{ma}{A} = k$$ $$k = 39 N/m$$