Question $2$

Consider the beam in Question $1$ with a hinge connection $($pinned$)$ at $\backslash ($ x$=0\backslash )$ and $\backslash ($ x$=1\backslash ).$

a$)$ Derive the beam's response if the force shown in Figure $2$ is applied at its midpoint.

b$)$ Plot the response at the beam's midpoint and at $\backslash ($ x$=0\mathrm{.}2\backslash$mathrm$\{$~m$\}\backslash )$ for $\backslash ($ t$=0\backslash )$ to $0\mathrm{.}5$ s using $\backslash (\backslash$mathrm$\{$N$\}=20\backslash )$ modes. Describe the responses. Do they differ and in what way? Figure $2.$ Force applied at the beam's midpoint.