Match the transfer function with correct Bode amplitude plots. G(s) = s+ 10 s(+100) s+ 100 G(s) = s(s+10) S G(s)= (s+10) (s+100) (+10) G(s) = (+100) s(+100) G(s) = (+10) (+10)(+100) G(s) = S A. -20 dB/dec 20 dB/dec B. D. 20 dB/dec -20 dB/dec 20 dB/dec -40 dB/dec -20 dB/dec 20 dB/dec 40 dB/dec E. 20 dB/dec -20 dB/dec 20 dB/dec 20 dB/dec -20 dB/dec

Match the transfer function with correct Bode amplitude plots. G(s)= S s²+7s+10 S G(s) = s² + 10s+ 100 s+1 G(s) = s²+10x+100 S+ 10 G(s) = G(s) = s²+s+10 s+ 10 s²+101s+ 100 A. 20 dB/dec -20 dB/dec B. -20 dB/dec -20 dB/dec C. 20 dB/dec 20 dB/dec E. 20 dB/dec -20 dB/dec -40 dB/dec -20 dB/dec

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)

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

Problem-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)

Which of the below Laplace transform pairs is correct? t of s+ 5 а. L{e 5t cos (4t)} (s + 5)2 + 16 Ob. L{e 5t cos (4t)} = - 4 (s + 4)2 + 25 s+5 L{e-5t cos (4t)} = (s - 5)2 + 16 s - 5 Od. L{e-St cos (4t)} = (s - 5)2 + 16

ASAP

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.

Find the inverse Laplace transform L-1{F(s)} of the function 10 F(s) : (s – 4)3 NOTE: The answer should be a function of t. L-{F(s)} =

The Laplace transform of f t.cos 4t s2-16 f (s) = f(s) = (s2+16)2 (s2+16)2 Option 1 Option 2 s+4 f (s) s+1 f(s) : (s2-16)2 (s2+4)2 O Option 3