The Hamiltonian of a 1D system is $H(q, p) = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 q^2 - \alpha q$. Hamilton's canonical equations of motion are:
(A)
\dot{q} = \frac{p}{m}, \quad \dot{p} = -m\omega^2 q + \alpha
(B)
\dot{q} = \frac{p}{m}, \quad \dot{p} = m\omega^2 q - \alpha
(C)
\dot{q} = p, \quad \dot{p} = -\omega^2 q
(D)
\dot{q} = \frac{p^2}{2m}, \quad \dot{p} = -\alpha