Question: Please write this question in matlab and find the roots by any of the root finding method (bisection, secant method, Newton-Raphson method and false-position method)
Please write this question in matlab and find the roots by any of the root finding method (bisection, secant method, Newton-Raphson method and false-position method)
Natural Vibration of a Uniform beam The natural vibration frequencies of a uniform solid beam with one fixed and one free end is given by 1+()( )=0 Where =(2)14 is the mass density, S is the cross-sectional area, is the natural vibration angular frequency, E is the modulus of elasticity (Youngs Modulus), and I is the cross-sectional area moment of inertia. In this problem, E and are material properties, and S,I and L depend on the shape of the beam itself. Also, cosh() is the hyberbolic cosine function. This equation would be derived commonly in must junior/senior-level vibration analysis courses for engineers. Values for a particular steel beam are given: =7.803 =158 2 =200 =1.315103 =3 (Some conversion to standard units may be necessary) Use any of the 4 root finding methods we discussed this week find the 2 smallest (but greater than 0) natural vibration frequencies to the nearest Hertz in a steel beam connected in this fashion (Note: the relationship between angular frequency and frequency is =2). For each method, a good starting guess will be necessary. (This problem will not be auto-graded). (Note: You will need to run your method twice to get both frequencies with a different set(s) of starting guesses)
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