**Prob. Set 8 due November 30**

**Problems:**

**1) Derive expressions for the Fourier Series coefficients A _{n}
and B_{n} as outlined in class. Trigonometric identities you might
find useful:**

**2sin(A)sin(B) = cos(A-B) - cos(A+B)**

**2cos(A)cos(B) = cos(A+B) + cos(A-B)**

**2sin(A)cos(B) = sin(A+B) + sin(A-B)**

**2) 6-14 (omit part a)**

**3) 6-15a**

**4) 6-15b**

**5) A flexible string of length L is stretched with equilibrium tension
T between fixed supports. Its mass per unit length is **m.
The string is set into vibration with a hammer blow which imparts a transverse
velocity v_{o} to a small segment of length a at the center. Find
the amplitudes of the lowest three harmonics excited.