Please answer all parts of the question and show all work Fsction lI: Free Response1. The figure below shows a block of mass m (Block 1) that is attached to one end of an ideal spring of force constant k and naturallength L. The block is pushed so that it compresses the spring to 3/4 of its patural length and is then released from rest. Just asthe spring has extended to its natural length L, the attached block collides with another block (also of mass m) at rest on ukinetic energy at impact is divided between Block 1 and Block 2. The collision sends Block 2 over the edge of the table, where tefalls a vertical distance H, landing at a horizontal distance R from the edge.Block 1LBlock 2km'm'HRWhat is the acceleration of Block 1 at the moment it's released from rest from its initial position? Write your answer interms of k, L, and m.(a)(b)If v, is the velocity of Block 1 just before impact, show that the velocity of Block 1 just after impact is(c)Determine the amplitude of the oscillations of Block 1 after Block 2 has left the table. Write your answer in terms of Lonly.Determine the period of the oscillations of Block 1 after the collision, writing your answer in terms of T, the period ofthe oscillations that Block 1 would have had if it did not collide with Block 2.(d)(e)Find an expression for R in terms of H, k, L, m, and g.2. A bullet of mass m is fired from a non-lethal pellet gun horizontally with speed v into a block of mass M initially at rest, at theend of an ideal spring on a frictionless table. At the moment the bullet hits, the spring is at its natural length, L. The bulletbecomes embedded in the block, and simple harmonic oscillations result.

1. The figure below shows a block of mass m (Block 1) that is attached to one end of an ideal spring of force constant k and natuta. length L. The block is pushed so that it compresses the spring to 3/4 of its natural length and is then released from rest. Just as the spring has extended to its natural length L, the attached block collides with another block (also of mass m) at rest on ue cube of the frictionless table. When Block 1 collides with Block 2 half of its kinetic enerey is lost to heat; the other half of Block 1 kinetic energy at impact is divided between Block 1 and Block 2. The collision sends Block 2 over the edge of the table, where falls a vertical distance landing at a horizontal distance R from the edge. Block 1 L Block 2 k m m H R (a) · What is the acceleration of Block 1 at the moment it's released from rest from its initial position? Write your answer in terms of k, L, and m. 2 (b) If v, is the velocity of Block 1 just before impact, show that the velocity of Block 1 just after impact is (c) Determine the amplitude of the oscillations of Block 1 after Block 2 has left the table. Write your answer in terms of L only.

1. The figure below shows a block of mass m (Block 1) that is attached to one end of an ideal spring of force constant k and natuta. length L. The block is pushed so that it compresses the spring to 3/4 of its natural length and is then released from rest. Just as the spring has extended to its natural length L, the attached block collides with another block (also of mass m) at rest on ue cube of the frictionless table. When Block 1 collides with Block 2 half of its kinetic enerey is lost to heat; the other half of Block 1 kinetic energy at impact is divided between Block 1 and Block 2. The collision sends Block 2 over the edge of the table, where falls a vertical distance landing at a horizontal distance R from the edge. Block 1 L Block 2 k m m H R (a) · What is the acceleration of Block 1 at the moment it's released from rest from its initial position? Write your answer in terms of k, L, and m. 2 (b) If v, is the velocity of Block 1 just before impact, show that the velocity of Block 1 just after impact is (c) Determine the amplitude of the oscillations of Block 1 after Block 2 has left the table. Write your answer in terms of L only.