Use receptance coupling to rigidly join two free-free beams and find the freefree assembly's displacement-to-force tip receptance. Both steel cylinders are described by the following parameters: \(12.7 \mathrm{~mm}\) diameter, \(100 \mathrm{~mm}\) length, \(200 \mathrm{GPa}\) elastic modulus, and \(7,800 \mathrm{~kg} / \mathrm{m}^{3}\) density. Assume a solid damping factor of 0.0015 . Once you have determined the assembly response, verify your result against the displacement-to-force tip receptance for a \(12.7 \mathrm{~mm}\) diameter, \(200 \mathrm{~mm}\) long free-free steel cylinder with the same material properties. Select a frequency range that encompasses the first three bending modes and display your results as the magnitude (in \(\mathrm{m} / \mathrm{N}\) ) vs. frequency (in \(\mathrm{Hz}\) ) using a semilogarithmic scale.