Answer to Question #217219 in Classical Mechanics for udara

Question

2. A mass 𝑚 rests on a frictionless horizontal table and is connected to rigid supports via two identical springs each of relaxed length 𝑙0and spring constant 𝑘, as shown in Fig. 2. Each spring is stretched to a length 𝑙 considerably greater than 𝑙0. Horizontal displacements of 𝑚 from its equilibrium position are labeled 𝑥 (along AB) and 𝑦 (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 𝑦 << 𝑙. (c) In terms of 𝑙 and 𝑙0, calculate the ratio of the period of oscillation along 𝑥 and 𝑦. (d) If at 𝑡 = 0 the mass 𝑚 is released from the point 𝑥 = 𝑦 = 𝐴0with zero velocity, what are its 𝑥 and 𝑦 coordinates at any later time 𝑡? (e) Draw picture of the resulting path of 𝑚 under the conditions of part (d) if = 9𝑙0/5.

Answer 1

Dear udara, your question requires a lot of work, which neither of our experts is ready to perform for free. We advise you to convert it to a fully qualified order and we will try to help you. Please click the link below to proceed: Submit order