A mass \(m\) is supported by two sets of springs oriented at \(30^{\circ}\) and \(120^{\circ}\) with respect to the \(X\)-axis, as shown in Fig. 2.66. A third pair of springs, each with a stiffness of \(k_{3}\), is to be designed so as to make the system have a constant natural frequency while vibrating in any direction \(x\). Determine the necessary spring stiffness \(k_{3}\) and the orientation of the springs with respect to the \(X\)-axis.

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eelle K2 k 00000 m 45 45 FIGURE 2.65 Mass restrained by four springs. x