A slackline is stretched between two trees at a distance, , so that a tensioning force, , is applied on the empty rope. A man then balances in the middle of the rope and exerts a weight force, , onto the slackline. What is the vertical deflection, , of the rope?
Details and Assumptions: The rope is made of an elastic material and obeys Hooke's law where is the force along the rope, is the initial length, is the stretched length of the rope, and is the force constant.