Assignment:
Use the method of separation of variables to show that the wave equation
has solutions of the form
What is a normal mode of a string? State two properties of normal modes that make them useful in the analysis of oscillating systems.
A string in which transverse displacements propagate at speed c has its ends fixed at x = 0 and x = IC. The midpoint of the string is drawn aside a small distance h and gently released. Show that at any subsequent time t the displacement is
What is the ratio of the energies contained in the fundamental and third normal modes?
Provide complete and step by step solution for the question and show calculations and use formulas.