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)
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.