The tapered circular shaft shown in Figure 5.23 is subjected to a longitudinal vibration, for which.

The tapered circular shaft shown in Figure 5.23 is subjected
to a longitudinal vibration, for which the EI term in the strain energy is
replaced by EA and Ψ″ is replaced by du/dx. Using Rayleigh’s method,
approximate the lowest natural frequency of this shaft. Let us assume that the
displacement is approximated by u(x) = A sin(πx/2L)