# Imagine, if you will, a baby jumper seat that is suspended from a porch beam. To provide…

Imagine, if you will, a baby jumper seat that is suspended from a porch beam. To provide additional stimulation, a music box, mass my, is suspended from the beam with a spring. The baby seat, mass m2, is suspended below the music box by another spring. The purpose of this problem is to explore what happens to the springs as the baby begins to jump in the seat. Two masses, m; and m2 are connected to two springs A and B as shown in the accompanying sketch X;=0 mi X2 = 0 Assume negligible mass for the two springs. The spring constants k, and k describe springs A and B, respectively. Let xi(t) and xa(t) represent the vertical displacements of the masses from their equilibrium positions. When t = 0, these are at equilibrium. When the system is in motion, spring B is subject to both an elongation and a compression, hence its net elongation is X2-X1. Therefore, it follows Hooke’s Law that springs A and B exert forces – kaxi and ko(x2 – x1). respectively, on mi. If no external force is impressed on the system and if no damping force is present, then the net force exerted on my is – kyx1 + kz(x2-x.). By Newton’s Second Law we can write -kax+ k(x2 – x). (DE 1) midt Similarly, the net force exerted on my is due solely to the net elongation of spring B; that is ka (x2 – xy).Thus it follows that m2 de – Ky(x2 – x1). (DE 2) Given the following assumptions:k = 6, K2 = 4, m1 = 1, m2 = 1 and that the masses start from their equilibrium positions with opposite unit velocities, determine the solution to the system of two differential equations. Hint: Start with the La Place transform of each equation Submission Instructions: Writing must follow proper rules of grammar and mechanics of writing in APA format. Appropriate referencing and citation is expected. • Show all work and provide a detailed explanation. An answer without any explanation will not receive credit. . If you have questions, ask your instructor.

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