A mass $m$ is connected to two zero-length springs of spring constants $k_1$ and $k_2$. The other ends of the springs are attached to frictionless bearings mounted on two parallel horizontal poles, with the upper pole a vertical distance $L$ directly above the lower pole. Each bearing slides freely along its own pole. The mass swings in a vertical circle of radius $R$ in a plane perpendicular to both poles. Assume the diameters of the poles and the rest lengths of the springs are negligible compared to $R$ and $L$. What is the vertical distance $h$ between the upper pole and the center of the circular orbit?