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i need the answers to part d) e) and f) - i have provided the solutions to the previous parts to help you with d) e) and f) , dare i say it again, I NEED PARTS d) e) and f)!!!!
. A dynamical system is composed of two bodies of masses m₁ and m2, which are placed on a horizontal non-smooth surface, and three springs with Hooke's constants ka k and ke, respectively, as shown in the figure. The motion of the two bodies is damped by friction with the surface, which is proportional to their velocities, with coefficients ₁ and ₂ respectively. The displacements of the two bodies with respect to equilibrium are denoted by r(t) and r2(t) re- spectively (these displacements are small enough that the springs remain in the linear regime, consistently with Hooke's law, throughout the motion). mm. ka kb kc H₂ H₂ (a) Determine the total force acting on each of the two bodies. (b) Write down the equation of motion of the system for the vector z(t) = (26))in in a matrix form. (c) Assume from now on that m₁ = m₂ = m, and ka = k = k = k and also #₁=₂ μ. Show that the equation of motion can be brought to the form: 2 d [()² + 2x +³²U]2(1) = 0 where U is a matrix and determine A, w and U in terms of u, k and m. (d) Define new coordinates y(t) = (36)) with r(t) = Ry(t) where R is a (time independent) matrix such that the equation of motion for y(t) is diagonal. Determine R and the new equation of motion. (e) Find the general solution for y(t) assuming that the parameters are such that one mode is over-damped and the other is under-damped. What is the range of values of w/A allowing this? (f) Determine the general solution for x₁(t) and x₂(t).
So, we have the two difmandal s 16 Mon, Considering, y= and 2 = = then, we got "1st onder det er? je (mz+(47) - ₂+(+₂)2₂-K₂X₂=0 m₂ ₂ + (₂+1) 4₂-M₂4 +K 4-0 are the Ras (6), the matic- 1 0 01 00 ODD M₂ +4 00 00 PP 0 hu 0 12 k E 0 5- (04) - (5) - (*) 6 G=N+AW SA lại tin nay là ko học kinh lại đây đ the tage m²*²²2*xx-xx- →*+*+,x= x + 2x² +w²vx =0 [² + 2x² + ²] x² = 0 A =xx son TY . The X