Question

The following is the longitudinal characteristic equation for an F-89 flying at 20,000 feet at Mach 0.638. The Short Period natural frequency is _____.

Answer 1

hello your question is incomplete attached below is the missing part

answer : short period oscillations frequency = 0.063 rad / sec

phugoid oscillations natural frequency (
`w_(np)` ) = 4.27 rad/sec

Step-by-step explanation:

first we have to state the general form of the equation

=
`( S^2 + 2\alpha _(p) w_(np) S + w^(2) _(np) ) (S^(2) + 2\alpha _(s) w_(ns)S + w^(2) _(ns) ) = 0`

where :

`w_(np) = Natural frequency of plugiod oscillation`

`\alpha _(p) = damping ratio of plugiod oscilations`

comparing the general form with the given equation

`w^(2) _(np)` = 18.2329

`w^(2) _(ns) = 0.003969`

hence the short period oscillation frequency (
`w_(ns)` ) = 0.063 rad/sec

phugoid oscillations natural frequency (
`w_(np)` ) = 4.27 rad/sec