 actuated pendulum whose base (pivot of the rod) is forced to oscillate horizontally according to the harmonic law $h \sin(\omega t)$, where $h$ denotes the amplitude of the oscillation and $\omega$ the frequency.  The equation of motion for this system is $$m l^2 \ddot \theta + m g l \sin \theta = m l \omega^2 h \sin (\omega t) \cos \theta + u.$$  (If this equation seems obscure to you, try to derive it using the <a href="multibody.html">Lagrangian approach</a>; but be careful, the kinetic energy $T(\theta