solving nonlinear algebraic equations where is related to important beam parameters through % ei where is the density of the beama is the area of the cross sectione is young' modulusand is the moment of the inertia of the cross section the most important parameter of interest is !which is the frequency of the beam we want to compute the frequencies of vibrating steel beam with rectangular cross section having width mm and height mm the density of steel is kg/ and  pa the moment of inertia of rectangular cross section is bh = aplot the equation to be solved so that one can inspect where the zero crossings occur hint when writing the equation as vd the function increases its amplitude dramatically with it is therefore wise to look at an equation with damped amplitudeg vd vd plot instead bcompute the first three frequencies filenamebeam_vib py open access this is distributed under the terms of the creative commons attributionnoncommercial international license (which permits any noncommercial useduplicationadaptationdistribution and reproduction in any medium or formatas long as you give appropriate credit to the original author(sand the sourcea link is provided to the creative commons license and any changes made are indicated the images or other third party material in this are included in the work' creative commons licenseunless indicated otherwise in the credit lineif such material is not included in the work' creative commons license and the respective action is not permitted by statutory regulationusers will need to obtain permission from the license holder to duplicateadapt or reproduce the material