Obtain the free response of 2x + 128x = 0 a) In the cartesian form b) In the form of sine x(t) = A₁sin (wnt) + A₂cos(wnt) x(t) = Asin(wnt+p) The initial conditions are x(0) = 0.05 m and x(0) = −0.3 m/s.
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- Note: handwritten solutions are strictly prohibited...Draw the signal flow graph of the following block diagram, then find the transfer function using Mason's rule R a G₁ H₁ H₂ G₂ +Q1/ Find L[t et sin t] Q2/ Find The Laplace Transform f(t) = [sint [sint 0Derive the set of differential equations for a three mass-four sprang system as shown in Figure below that describes their time motion. Write the three differential equations in matrix form as figure attachment.8Find the Laplace Transform of the following functions 1) f() cos(ar) Ans. F(s)=7 2ws 2) f() sin(at) Ans. F(s)= s² + a² 3) f(r)-rcosh(at) Ans. F(s)= 2as 4)(t)=sin(at) Ans. F(s)= 2 5) f(1) = 2te' Ans. F(s)= (S-1) 5+2 6) (1) e cos() Ans. F(s) = (+2)+1 7) (1) (Acostẞr)+ Bsin(Br)) Ans. F(s)- A(s+a)+BB (s+a)+B 8) f()-(-)() Ans. F(s)= 9)(1)(1) Ans. F(s): 10) f(r),()sin() Ans. F(s): 11) 2 k 12) 0 13) 0 70 ㄷ.. a 2a 3a 4a 2 3 4 14) f(1)=1, 0<1<2 15) (1) Ksin(t) 0All values equal to 1= = Problem #2 - Modeling, Mass-Spring System Two masses are connected by springs in series as shown in Figure 1 below where k₁ 20 N/m, k₂ = 10 N/m, m₁ 10 kg, and m₂ = 5 kg. Solve the system of ODEs in matrix form using the determinant to obtain the characteristic equation (it will make sense to substitute > for w² when you get to your characteristic equation). Determine the eigenvalues (frequencies) and eigenvectors (modes) of oscillation. Assume that no damping is present and that the masses slide without friction. On your diagram, sketch the modes of oscillation (think of how the masses could oscillate with respect to each other). What determines which mode or combination of modes that the masses oscillate at? i.) ii.) iii.) iv.) v.) vi.) vii.) Sketch the system and include a free body diagram. Use a conservation equation to develop your differential equation model (you should end up with two ODEs to describe the motion of both masses). Write your system of ODEs in matrix form. Set…Problem 1: Laplace Transforms For a spring-mass-damper system with the following characteristics m = 70 k= 707 C = 69 Xo = 0 m/s Vo = 0 m/s If an forcing function F(t) = 100tet N is applied to the box at t = 0s, find x(t) for the system analytically. HINT: I STRONGLY suggest that you use the Laplace transform method. Please box your final x(t), and plot your solution.SEE MORE QUESTIONSRecommended textbooks for youElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
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