Answer
$1.2m/s$
Work Step by Step
We can find the required speed as follows:
$\omega_n=\sqrt{\frac{K}{m}}$
$\implies \omega_n=\sqrt{\frac{2\times 800}{450}}$
$\implies \omega_n=1.8856rad/s$
We know that
$T=\frac{2\pi}{\omega_n}$
$\implies T=\frac{2\pi}{1.8856}$
$\implies T=3.3322s$
Now $v=\frac{\lambda}{T}$
We plug in the known values to obtain:
$v=\frac{4}{3.3322}$
$\implies v=1.2m/s$