Consider a system $($not pictured$)$ described by

$[[2,1],[1,1]][[$x$\_(1)^()],[$x$\_(2)^()]]+[[3,1],[1,1]][[$x$\_(1)],[$x$\_(2)]]=[[1],[1]]$f$($t$)$

It can be shown that the above system has mode shapes vec$($u$)\_(1)=$C$\_(1)[[0,1]]^($T$)$ and vec$($u$)\_(2)=$C$\_(2)[[1,-1]]^($T$),$ where C$\_(1)$

and C$\_(2)$ are arbitrary constants $($the mode shapes have not yet been normalized with respect to the mass$).$

Please answer the following questions.

aG$($j$\backslash$omega $)$ starting from physical coordinates.

bG$($j$\backslash$omega $)$ starting from modal coordinates.

cx$\_(2).$ What must the frequency $\backslash$omega of the harmonic force be

such that x$\_(2)($t$)=0$ at steady$-$state? Will the magnitude of the harmonic force affect the response of x$\_(2)$ at

this frequency?

ex$\_(1)$ and measuring the physical response

of x$\_(2).$ Will you be able to identify the first resonant frequency from the frequency response? Why or why not?