Complete all tasks in an M-file, which is executed at the command line except as indicated. (1) Write 2 MATLAB functions, which solve f(x=0, where is an arbitrary function using la) the bisection method, and (b) Newton's method. Each should have suitable starting points and termination conditions Note: As usual, the only built-in functions that the function may use are some and abs. Other built-in MATLAB functions should not be used. If in doubt as to the use of a particular function, ask. Be sure to suppress all intermediate output in the function using semi-colons Document your code adequately. "Mysterious procedures will result in reduced assignment score. (2) Test your functions by combining them (one to help the second) to solve the following problem: Whirling shaft. An unbalanced disk on a rotating shaft will rotate eccentrically in its own plane if the shaft is simply supported with 2 bearings. If the shaft is overhanging, as shown in figure I below, it will whirt out of plane. H Figure 1 Let be the whirling speed of the shaft, and the speed of the shaft. The speed is called critical if it is one of the natural frequencies of the shaft. Note that cases (a) and (b) above will have different critical speeds even though the shaft stiffness as well as the disk masses may be the same. This is due to the fact that the centrifugal forces of the various particles of the disk do not lie in one plane. Cal Poly Pomona H Call Poly Pomona 4 Figure 2 The system can be modeled as shown in figures 3 and 4 below Figure Here Figure 4 so that the position of the disk is defined by the angle and the displacement mess of the disk 1. = moment of inertia of the disk about adiameter = poler moment of inertia of the disk about the deflected shaftcenterline Now, the elastic properties of the shaft are described by three influence numbers: