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{"ops":[{"insert":"2. A mass \ud835\udc5a rests on a frictionless horizontal table and is connected to rigid supports via two identical springs each of relaxed length \ud835\udc590and spring constant \ud835\udc58, as shown in Fig. 2. Each spring is stretched to a length \ud835\udc59 considerably greater than \ud835\udc590. Horizontal displacements of \ud835\udc5a from its equilibrium position are labeled \ud835\udc65 (along AB) and \ud835\udc66 (perpendicular to AB). (a) Find the angular frequencies of the normal modes for longitudinal oscillations of small amplitude. (b) Find the angular frequencies of the normal modes for transverse oscillations, assuming \ud835\udc66 << \ud835\udc59. (c) In terms of \ud835\udc59 and \ud835\udc590, calculate the ratio of the period of oscillation along \ud835\udc65 and \ud835\udc66. (d) If at \ud835\udc61 = 0 the mass \ud835\udc5a is released from the point \ud835\udc65 = \ud835\udc66 = \ud835\udc340with zero velocity, what are its \ud835\udc65 and \ud835\udc66 coordinates at any later time \ud835\udc61? (e) Draw picture of the resulting path of \ud835\udc5a under the conditions of part (d) if = 9\ud835\udc590\/5.\n"}]}

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