The amplitude of oscillation of the image is

Magnification, $m=\frac{h_i}{h_o}=\frac{v}{u}$  

$u=-3fv=d\frac{3}{2}f$     (solved earlier)

$\frac{h_i}{A}=\frac{\frac{3}{2}f}{-3f}$

$⟹h_i=-\frac{1}{2}A$      OR  $m=-\frac{1}{2}$

Image will also execute SHM according to equation, $y=\frac{A}{2}sin(wt+\pi )$ 

So amplitude of oscillation of image is $\frac{A}{2}$