Cantilever Beam: System Identification $($DAMPING$)$

Theoretical Values: me$=\mathrm{.}0055$kg and ke$=12\mathrm{.}50$ n$/$m

Measured Values:

Damping ratio $($zeta$)=\mathrm{.}0614$

Natural frequency$(\backslash$omega n$)=1314\mathrm{.}966$ rad$/$s

Parameter Identification:

$1.$ Using the theoretical value for : me to calculate the damping constant $($c$)$ and the spring constant k$,$ we get,

Damping constant, c $=\mathrm{.}16$kg$/$s and the spring constant k $=289\mathrm{.}076$ n$/$m

$2.$ Using the theoretical value for : ke to calculate the damping constant $($c$)$ and the mass$($m$)$ we get,

Mass$($m$)=\mathrm{.}000313$ Kg and Damping constant, c $=\mathrm{.}00804$kg$/$s

$3.$Using the theoretical value for : me and ke to calculate the damping constant $($c$),$ we get,

C$=0\mathrm{.}117$ kg$/$s

Discussion $(40$ points$)$

Q$1.$Please Compare the coefficients for all the previous answers above and explain Why they are different? Please note that the answer should relate to damping.

Q$2.$ Compare the values of theoretical natural frequency,

$\backslash$omega n$=1314\mathrm{.}966$ rad$/$s to that of the measured natural frequency

$\backslash$omega n$=286\mathrm{.}369$ rad$/$s$.$ Why are they different? Please note that the answer should relate to damping.