A homework question about Acoustics-Mechanical Engineering.

A string is free at x = 0 and given a harmonic displacement at Ae^iwt at x = -L.

a.) Solve for the string displacement y(x,t) and determine the resonance frequencies.

b.) Find the formula for the mechanical impedance at the drive point x = L.

c.) What does this impedance look like at low frequencies, and why? You can determine the answer to the following part using impedance:

d.) Now suppose the end at x = -L is fixed. Find the formula for the free vibration frequencies and the associated orthogonal mode shapes. Hint: What value must the impedance assume at the fixed end?