Hello there,
Could some one help me to find equations of motions of this problem attached to this message?
The technical name of that setup is a parametrically driven pendulum. The suspension point moves up and slightly, in a sinusoidal pattern. When the driving frequency is an exact match for the natural frequency of the pendulum the drive will sustain the pendulum oscillation.
A team of millersville University has build several small Foucault pendulums with parametric drive. See their "[URL discussion[/URL] of equations of motion for a parametrically driven pendulum..