According to the note on longitudinal short period approximation, assuming the nominal pitch angle is 0

d/dt [∆α/∆q] = [ Zα/U1 1 ] [∆α] + [ Zδe/U1 ] ∆δe
[ (Mα + Mα Zα/U1) (Mq + Mα) ] [∆q] [Mδe + Mα/U1 Zδe ]

Derive the 2nd order equation of ∆q only, in the following form

d²∆q/dt² + C d∆q/dt + K∆q = f

Where C, K, f must be written in terms of the stability derivatives in the matrices above as well as the elevator deflection angle