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Two identical particles are attached at the ends of a light string which passes through a hole at the center of a table. One of the particles is made to move in a circle on the table with angular velocity \( \omega_{1} \) and the other is made to move in a horizontal circle as a contact pendulum with angular velocity \( \omega_{2} \). If \( l_{1} \) and \( l_{2} \) are the length of the string over and under the table, then in order that particle under the table neither moves down nor moves up, the ratio \( l_{1} / l_{2} \) is
(1) \( \frac{\omega_{1}}{\omega_{2}} \)
(2) \( \frac{\omega_{2}}{\omega_{1}} \)
(3) \( \frac{\omega_{1}^{2}}{\omega_{2}^{2}} \)
(4) \( \frac{\omega_{2}^{2}}{\omega_{1}^{2}} \)
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