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by | Jun 24, 2023 | Posted Assignments

I need help with (d) and (e) please. I have (a) (b) and (c) but i’m not sure how to solve (d) or (e).

3-H A mass m rents on a frictionless horizontal table and is connectedto rigid supports via two identical springs each of relaxed length inand spring constant it (see ?aunt). Each spring is stretched to a length{considerably greater than in. Horizontal displacements of m from itsequilibrium position are labeled x (along AB) and y (perpendicularto A3). (a) Write down the di?‘erential equation of motion (i.e., Newton‘slaw) governing small oscillations in the x direction. (b) Write down the differential equation of motion governingsmall oscillations in the y direction (assume y («C I). (c) In terms of l and to, calculate the ratio of the periods ofoscillation along x and y. (d) Ifatt-t smisreleaeedfromthepointx=y=Aowith zero velocity, what are its x and y coordinates at any later time t? (e) Draw a picture of the resulting path of in under the condi- tions of part (a) if! = tan/5.

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