Find the eigenfrequency and normal Coordinates for the model below. 47 1 b سید 3₁ 19₂2 олишини と 30
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- nk int m The spring-mass-system shown in the figure has the following parameters: spring constant k = 4 N/m; mass m 6 %3D kg and the constant n = 1.6. M is the corresponding mass-matrix of the system. V1 and V2 are the eigenvectors associated with the smallest and largest natural frequencies of the system, respectively. If V,TV, = 1 and V2 V2 = 1, then what is value of V,™MV2 (in kg)? Answer:össlg äbäi What is the the transfer function of the first-order system which has the impulse response curve as in * ?the following figure Impulse Response 1.8 1.6 1.4 1.2 System: sys Time (seconds): 0.333 Amplitude: 0.737 1 0.8 Slop 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (seconds) 1/(s+3) O 2/(s+3) O 6/(s+3) O No one of the answers in a, b, and c ( Amplitude 2.1. A force F is applied to the mass m₂ in Figure 1, where k₁ and k₂ are the spring constants, b₁ is the damping constant and b₂ is the friction coefficient, x₁ and x₂ are the displacement. Find the transfer function X₁/F. K₁ wwww no chat GPT, HAND WRITTEN PLEASE m1 X1 b₁ + K₂ No friction Figure 1 M₂ X2 Friction b₂ LL F
- Figure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.(1) Consider the system represented by the block diagram. The closed loop transfer function T(s)-Y(s)/R(s) is (a) T(s)-50/(s+55 s+50). (b) T(s)=10/(s+50 s+55) (c) T(s)=10/(s+55 s+10). (d) None of the above. R(s)- 10 + s+5 5 Y(s)Compute the Laplace Transforms of the following time domain functions from the Laplace Transformation definition a) f(1) =r" b) f(t) =tcos(wt)
- For the following open loop transfer functions, identify the correct Bode plot from the Bode plots given below: Bode Plots: Magnitude (dB) Phase (deg) O 50 -100 -50 -150 -90 0 -135 -180 Magnitude (dB) a 225 Phase (deg) -270 -20 10:2 -40 -60 -80 -100 0 -90 -180 G(s) = -270 Transfer function: a. 1 10-1 101 O b. 2 O c. 3 O d. 4 S Bode Diagram 10° Frequency (rad/s) Bode Diagram (₁² +s+2)(x² +58 + Frequency (rad/s) s+16) 101 10¹ 10² % 2) Magnitude (dB) Phase (deg) Magnitude (dB) Phase (deg) 50 -50 -100 -45 -90 -135 -180 10/2 -60 -80 -100 -120 90 0 -90 -180 -270 10:2 10¹ 10" Bode Diagram 10° Frequency (rad/s) Bode Diagram 10° Frequency (rad/s) 10¹ 101 10² 102Draw the signal flow graph of the following block diagram, then find the transfer function using Mason's rule R a G₁ H₁ H₂ G₂ +For the following open loop transfer functions, identify the correct Bode plot from the Bode plots given below: Bode Plots: 1) 3) Magnitude (dB) (Bap) eseyd 50 0 -100 -50 -150 -90 -135 -180 Magnitude (dB) -225 Phase (deg) -270 1012 -20 -40 -60 -80 -100 0 -90 -180 -270 G(s) = 10-1 Transfer function: 10 O a. 1 O b. 2 O c. 3 O d. 4 16 Bode Diagram TOP Frequency (rad/s) Bode Diagram (s+4)(s² +1.65+4) 101 Frequency (rad/s) 10 Њ 10² 10² N + Magnitude (dB) Phase (deg) Magnitude (dB) Phase (deg) 50 -50 -100 -45 -90 -135 -180 10:12 -20 -40 -60 -80 -100 -120 90 0 -90 -180 -270 1012 10 10 Bode Diagram 10² Frequency (rad/s) Bode Diagram 10² Frequency (rad/s) 10 10¹ 10² 10²
- For the system represented by the following government equations in matrix form: Determine the forced response of the system [2k -c*2+-k [Focoswt] [m [2c -k *2+-c ml Li3. -k||x2 = [x3] m 2c 2k -kA proposed hypersonic plane would climb to 100,000 feet, fly 3800 miles per hour, and crossthe Pacific in 2 hours. Control of the aircraft speed could be represented by the model in Figure.Find the sensitivity of the closed-loop transfer function T(s) to a small change in the parameterProblem-3. Consider the closed loop transfer function from R(s) to C(s) as given below as given below. 85 H(s) = (s+5)(s? + 2s +17) MATLAB gives the partial fraction values of the Laplace transform C(s) to the unit step input as follows: Num: Denom: -0.5313 -5.0000 -0.2344 + 0.3906i -1.0000 + 4.0000i -0.2344 - 0.3906i -1.0000 - 4.0000i 1.0000 d) Find the overshoot and peak time by using the reduced-order transfer function Hint:Tp = e-(n{//1-§2 %OV = Wn V1- 2)