Answer
.69 seconds
Work Step by Step
We must find the period of the oscillations:
$ T = \frac{2\pi}{\omega}=\frac{2\pi}{\sqrt{\frac{k}{m}}}=\frac{2\pi}{\sqrt{\frac{2.2}{.43}}}=2.78 \ sec $
We know that $\pi/2$ is one quarter of a period, so it follows:
$ t = \frac{2.78}{4} = \fbox{.69 seconds}$
