A 2.70-kg block is suspended from a spring with a spring constant of 180.0N/m. A 0.090-kg bullet is fired into the block from directly below with a speed of 110.0m/s and is embedded in the block. Find the amplitude of the subsequent motion. You may ignore gravitational potential energy as if the system was horizontal (which turns out not to be an approximation--doing so yields exactly correct results!) and initially at rest with the block resting at the equilibrium length of the spring. Also assume that the during the very short time of the collision, until the bullet stops moving with respect to the block, the block only moves by a negligible amount. What fraction of the original kinetic energy of the bullet appears as mechanical energy in the system of block-spring-bullet?