Given, mass of the particle, $m=0.4 \mathrm{~kg}$
Amplitude, $A=0.4 \mathrm{~m}$
Initial phase, $\phi=\frac{\pi}{4}$
Kinetic energy at mean position $\mathrm{KE}$
As,
$$
\begin{aligned}
& =256 \times 10^{-3} \mathrm{~J} \\
\mathrm{KE} & =\frac{1}{2} m \omega^2 A^2
\end{aligned}
$$
where, $\omega$ is angular frequency.
$$
\begin{array}{cc}
\Rightarrow & \frac{1}{2} m \omega^2 A^2=256 \times 10^{-3} \\
\Rightarrow & \frac{1}{2} \times 0.4 \times \omega^2 \times(0.4)^2=256 \times 10^{-3} \\
\Rightarrow & \omega^2=8 \\
\Rightarrow & \omega=2 \sqrt{2} \mathrm{rad} \mathrm{s}^{-1}
\end{array}
$$
Equation of simple harmonic motion is given by
$$
\begin{aligned}
x & =A \sin (\omega t+\phi) \\
& =0.4 \sin \left[(2 \sqrt{2}) t+\frac{\pi}{4}\right]
\end{aligned}
$$