Answer
$2.57 \hspace{1mm}s$.
Work Step by Step
Restoring force of the spring $=-kx$, where $k$ is the spring constant. Mass of the object $=M=0.400\hspace{1mm}kg$
Force on the object $=0.400\times a_x= 0.400\times\hspace{2mm}(-1.80)\hspace{1mm}N$.
This is equal to $-0.72\hspace{1mm}N$.
$x=0.300\hspace{2mm}m$. Thus,
$\hspace{7mm}-kx=-0.72\\
\Longrightarrow k(0.300)=0.72\\
\Longrightarrow k=2.4\hspace{2mm}N/m$
The time for one oscillation is the time period ($T$).
$T=2\pi\sqrt{\large \frac{M}{k}}$
Putting all the values we get $T\simeq2.57\hspace{1mm}s$.
