Answer
$$k = 39 N/m$$
Work Step by Step
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:
$$ F = kA$$
$$\frac{ma}{A} = k$$
$$k = 39 N/m$$