(2.6.7) tan(0) kL B.(k) KL tan(kL + ) = B. (k) and both these equations must be solved for k to obtain the mode shape. Homework Problem: Solve the dispersion relationship 2.6.7 for a cable with a mass at each end that are 2 and 3 times the weight of the cable at x=0 and x=L respectively. To do this write a MATLAB program that defines the function f(KL)= tan kL - tan KL B. (k) ) KL B. (k) at values of k=mAkL over a suitable range to obtain the first five modes. Plot this function to identify the zero crossing points. Using fm=f(mAkL) search for the zeroes of this function by forming the product Pn=fnfm+ 1 and using the find command j=find(p