Physics 213 November 16, 1999

Prob. Set 8 due November 30


1) Derive expressions for the Fourier Series coefficients An and Bn 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 vo to a small segment of length a at the center. Find the amplitudes of the lowest three harmonics excited.