Problem $2$

The cantilever beam shown in Fig. $3$ carries a concentrated weight at its free end and it is subjected to a periodic acceleration at its support which is the rectified sine function of period $\backslash (\backslash$mathrm$\{$T$\}=0\mathrm{.}4\backslash$mathrm$\{$sec$\}\backslash )$ and amplitude $\backslash (\backslash$ddot$\{$y$\}\_\{$g$\}=180\backslash$mathrm$\{$in$\}/\backslash$mathrm$\{$sec$\}^\{2\}\backslash )$ as shown in Fig. $4.$ Determine: $($a$)$ the Fourier series expansion of the forcing function, and $($b$)$ the steady$-$state response considering only three terms of the series. Neglect damping in the system and assume the beam massless.

Problem $3$