How to slove part b numirically matlab code needed$(15$ points$)$ A cable of length $l$ and mass $$ per unit length is stretched under a tension $P.$ One end of the cable is connected to a mass $m,$ which can move in a frictionless slot, and the other end is fastened to a spring of stiffness $k,$ as shown in the Figure $1.$

$($a$)$ Derive the frequency equation for the transverse vibration of the cable.

$[$Ans: $[$:$tan(\frac{l}{c})=\frac{Pc}{}(\frac{k-m{}^2}{m{c}^{2}k+P^2})\}.$

$($b$)$ Solve for the first five natural frequencies assuming the following data: $l=1m,P=1000N,=0\mathrm{.}1k\frac{g}{m},m=20kg$ and $k=5000\frac{N}{m}.$

$[$Ans: ${}_1=6\mathrm{.}4486ra\frac{d}{s},{}_2=265\mathrm{.}53ra\frac{d}{s},{}_3=545\mathrm{.}52ra\frac{d}{s},{}_4=839\mathrm{.}19ra\frac{d}{s},$ and ${}_5=$

Figure $1$: Cable connected to mass at one end and springs at the other end