Question

QUESTION9 2Marks) The fundamental mode of vibration (first harmonic) of a support cable in a suspension bridg may be used to determine the tension in the cable. An engineer measures the fundamental frequency and her calculations show the design specs for the mast. By what fraction will the tension in the cable change if the frequency was made 4% higher? that the frequency should be 4% higher in order to meet

Answer 1

Solution ) fundamental frequency f= (1/2L)(T/u)^(1/2)

Frequency f is directly proportional to (T)^(1/2)

f changes by small % that is 4% so tension T changes as

df/f = (1/2)dT/T

4 = (1/2)dT/T

dT/T = 8%