One end of a light elastic string of natural length \(0.5\) m and modulus \(14\) N is attached to a fixed point \(A\) on a smooth plane. The plane makes an angle \(\alpha\) with the horizontal, where \(\tan\alpha=\frac{7}{24}\). A particle \(P\) of mass \(2\) kg is attached to the other end. The string lies along a line of greatest slope. Initially, \(P\) is held above the level of \(A\), where \(AP=0.8\) m, and is then released from rest.

Find the maximum velocity of \(P\) during the subsequent motion.