Start with Etkin, Problem $5\mathrm{.}2,$ but instead explicitly compute the individual values for $C_{m_q}$ and $C_{m_{{}^{}}}$ if experimental data with wind tunnel on led to measurements of ${}_n=2\mathrm{.}6451ra\frac{d}{s}$ and $=0\mathrm{.}5655.$ Use the following data:

ISA, sea level

Mach $0\mathrm{.}158$

$W=2750lb$

$S=184f{t}^2$

$b=33\mathrm{.}4ft\frac{?}{b}$

$ar(c)=5\mathrm{.}7ft$

$I_y(atc\frac{g}{s}$pring hinge $)=3000$ slug $f{t}^2$

$C_{L_{}}=\frac{4\mathrm{.}44}{r}ad$

$C_{D_0}=0\mathrm{.}05$

$C_{m_{}}=-\frac{0\mathrm{.}683}{r}ad$

Let ${}_0=0$rad

First find the rotational spring stiffness of the test fixture in $\frac{ftlb}{r}ad$ such that, with the wind tunnel off, ${}_n$ of this SDOF system corresponds to an undamped period of $60$ sec $.$