QUESTION 3Consider a system model given byd²x (t)dx (1)dt²dtx (0) = 1dx (t)dt3eWhat is the impulse response function?sint-21- 4e3e+4-=0sint + e-21= 1.-2t-2tsint + esint + ecost- 2t+ 5x (t) =f(t)sint - 2ecost + 2-2t-21cost + 2costsint - 2cost + e-

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Answered: QUESTION 3 Consider a system model…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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5 Problem Match the following two frequency response diagrams: -0 0.4 |G(i w)| 0.2 10 |G(i w)| 5 Response A 2 3 4 5 6 7 8 Frequency, (rad/s) Response B 5 6 7 8 Frequency, w(rad/s) 1 2 3 4 6 6 10 10 10 to two of the following ODES 1. +x+100x = u(t) 5. +100x = u(t) 9. +100x = u(t) 3. x+x+5x= u(t) 4. x+x+x= u(t) 2. x+x+25x = u(t) : 6. x + 25xu(t) 10. +25x = u(t) 7. x+5x= u(t) 8. u(t) 11. +5x= u(t) = 12. xu(t)
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.
Let C be the line segment joining A(-1,1, -2) to 0(0,0,0). A parameterization of C is given by * O x=-t,y=t,z=-2t, Osts1 O x=-t+1,y=t+1,z=-2t-2, Osts1 O x=-t-1,y=t+1,z=-2t-2, Osts1 x=t-1,y=-t+1,z=2t-2, Osts1 None of these
Feedback & Control Systems State-Space Representation Write the state-space representation of the system below. Let the output of the mechanical system is x3 (t). 1 N-s/m x₁ (t) M3 = 1kg 1 N/m М1 -0000 1kg > X3 (t) 1 N-s/m 1 N/m oooo x₂ (t) M₂ 1kg 4 1 N-s/m² -1 N-s/m →f(t)
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QUESTION 2 Consider a system model given by d²x (t) d1² 2- + 3x (t) = 48 (t) x (0) = 1 dx (t) dt =0- = -3. What is the initial response at t=0+? x(0+)=0 and dx/dt(0+)= -1 x(0+)=1 and dx/dt(0+)= 4 x(0+)=1 and dx/dt(0+)= -1 x(0+)=2 and dx/dt(0+)= -1 x(0+)=1 and dx/dt(0+)= 1 x(0+)=4 and dx/dt(0+)= 1
Question 4 a) A control engineer has modelled the suspension system of a new model car using a 2nd order differential equation. Using Laplace Transform, the engineer has managed to work out the transfer function, which is given below: 0.001 s2 + 12s+81 What is the natural frequency, the damping ratio and the constant K of the system? Please show all calculations. b) The same engineer has studied the suspension system of a SUV vehicle and modelled it using again a 2nd order differential equation, which has resulted into the following 2nd order transfer function: Y(s) 32 U(s) 4s² +8s + 16 For this system first calculate the damping ratio and its natural frequency and state whether the system is underdamped, overdamped or critically damped. Then calculate the peak time, peak value, settling time and damped natural frequency of the system.
نقطة واحدة A first – order system and its response to unit step input as in Figure, what is the correct * ?transfer function Slop Step Response 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 2 4 8 10 12 14 16 18 Time (seconds) 1/(0.2 s+1) O 1/(0.5 s+1) 1/(s+1) O 1/(2 s+1) Amplitude
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1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…

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QUESTION 3 Consider a system model given by d²x (1) dx (1) d1² dt x (0) = 1 dx (1) dt +4 +5x (t) = f(t) r=0 What is the impulse response function? 'sint = 1. о зе sint+e -21 O 3e 'sint+e' O-4e-2¹ sint - 2e-21 cost -21 cost+2 -21 sint+e -21c sint - 2cost + e-¹ cost + 2 cost