Math 641-600 Extra Problems

• These problems are from the text.
  1. Problem 2, page 206 (§ 5.1).
  2. Problem 6, page 207 (§ 5.1).
  3. Problem 7, page 207 (§ 5.1).
• Hanging chain problem. A chain having uniform linear density ρ hangs between the points (0,0) and (1,0). The total mass m, which is fixed, and the total energy E of the chain are
  
  Assuming that the chain hangs in a shape that minimizes the energy, find the shape of the hanging chain.