(Lateral vibration of a bead on a string) Consider a mass m, such as a bead, restrained by...

(Lateral vibration of a bead on a string) Consider a mass m, such as a bead, restrained by strings (of negligible mass), in each of which there is a tension tq, as shown in Fig. a.

We seek the frequency of small lateral oscillations of m. A lateral displacement x (Fig. b) will cause the length of each string to increase from l0 to l(x) = a/(02 + x2. Suppose that the tension r is found, empirically, to increase with I, from its initial value tq, as shown in Fig. c.

Show that the governing equation of lateral motion is

Where is a function, not a product.