The piston in a large engine rises and falls in simple harmonic motion. When the piston is 1.6 m below its highest level, the rate of change of its height is \(\frac{3}{5} \pi\) metres per second. When the piston is 0.2 m below its highest level, the rate of change of its height is \(\frac{1}{4} \pi\) metres per second. Find the amplitude and period of the motion.