Simple harmonic motion question about amplitude

I am stuck on a question which describes that there is a particle $$P$$ of mass 0.6kg (which is not so relevant) attached to an elastic spring of natural length 2.5m. The other end of the spring is attached to a fixed point $$A$$ on the smooth horizontal plane on which $$P$$ lies. The particle is held at point $$B$$ where AB=4m and released from rest. The motion of the particle can be described using the equation $$x''=-\frac{50}{3}x$$ where $$x$$m is the displacement of $$P$$ from $$A$$. The question asks for the amplitude and period of the subsequent motion. How can the simple harmonic motion be taking place about centre $$A$$ and not the point 2.5m away from $$A$$ of the natural length of the spring especially since the amplitude is given as 1.5m in the answers?

• I think that the equation is $x''=-50x/3$ and not yours. – Luca Sep 11 at 18:20
• Yes sorry I edited it but the question still stands – TheWhizzz Sep 11 at 18:22
• Looks like a simple typo in the question to me. This is not unheard of. – amd Sep 11 at 18:26