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Linear Systems –
Medium Difficulty
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LET’S PRACTICE!
#1. The inverse Laplace transform of 1/(s²+4) is:
#2. The inverse Laplace transform of s/(s²+4) is:
#3. A higher Q factor indicates:
#4. The Q factor of a series RLC circuit with R=10Ω, L=1mH at resonance (f₀=5kHz) is:
#5. A system with impulse response h(t) = δ(t) – 2e^(-t)u(t) has transfer function:
#6. A type-1 system has _____ poles at s = 0:
#7. A system is stable if all poles of its transfer function are:
#8. The impulse response of H(s) = 1/(s+2) is:
#9. The Laplace transform of df/dt is:
#10. The Laplace transform of f(t) = cos(ωt) for t ≥ 0 is:
#11. The steady-state error to a unit step input for a type-0 system with DC gain K is:
#12. The damping ratio ζ of a critically damped second-order system is:
#13. The unit ramp response can be found by:
#14. The steady-state response to a sinusoidal input can be found using:
#15. The Routh-Hurwitz criterion is used to determine:
#16. A bandpass filter transfer function has:
#17. A pure time delay of T seconds in the s-domain is represented by:
#18. A first-order all-pass filter has the transfer function:
#19. The resonant frequency of a second-order system with ωn = 10 rad/s and ζ = 0.5 is:
#20. The time constant τ of a first-order system with transfer function H(s) = K/(τs+1) is:
#21. The roots of s²+5s+6 = 0 are:
#22. A system with H(s) = (s+1)/(s+2)(s+3) has:
#23. The poles of a transfer function H(s) = 1/(s+2)(s+3) are located at:
#24. For a transfer function H(s) = 10/(s²+4s+20), the DC gain is:
#25. The frequency response of a system is obtained by evaluating H(s) at:
#26. The step response of a system can be found by:
#27. The transfer function H(s) = Ks represents:
#28. The inverse Laplace transform of F(s) = 1/s² is:
#29. The Laplace transform of ∫f(τ)dτ from 0 to t is:
#30. For H(s) = K(s+z₁)/((s+p₁)(s+p₂)), if z₁ > p₁ > p₂, this is a:
#31. The natural frequency ωn of the system with poles at s = -2 ± j4 is:
#32. For F(s) = (s+3)/((s+1)(s+2)), the inverse Laplace transform contains terms:
#33. A first-order system has a pole at s = -5. The time constant is:
#34. The transfer function H(s) = K/s represents:
#35. A second-order system with ζ = 0 will exhibit:
#36. A system has H(jω) = 1/(1+jω). At ω = 1 rad/s, |H(jω)| equals:
#37. The frequency response magnitude |H(jω)| at very high frequencies for H(s) = 1/(s+1) approaches:
#38. At resonance in a parallel RLC circuit, the impedance is:
#39. At resonance in a series RLC circuit, the impedance is:
#40. The forced response of a system is determined by:
#41. The percent overshoot of a second-order underdamped system depends on:
#42. The characteristic equation of a system with H(s) = K/(s²+5s+6) is:
#43. The Laplace transform of f(t) = sin(ωt) for t ≥ 0 is:
#44. The bandwidth of the series RLC circuit in the previous question is:
#45. A lead compensator has a transfer function of the form:
#46. An underdamped second-order system has a damping ratio ζ:
#47. The transfer function H(s) of a system is defined as:
#48. The rise time of a first-order system with time constant τ is approximately:
#49. The Laplace transform of the unit impulse function δ(t) is:
#50. The Laplace transform of f(t) = e^(-at) for t ≥ 0 is:
#51. The frequency at which |H(jω)|² = 0.5|H(0)|² is called:
#52. The region of convergence (ROC) for a causal system:
#53. The magnitude of H(jω) at ω = 0 is called:
#54. A system is called causal if:
#55. The final value theorem states that f(∞) equals:
#56. For a series LC circuit (no resistance), the natural frequency is:
#57. For a system to be stable, all coefficients of the characteristic polynomial must be:
#58. At ω = 1 rad/s for H(jω) = 1/(1+jω), the phase angle is:
#59. The Laplace transform of t·e^(-at) is:
#60. The settling time (2% criterion) of a first-order system with time constant τ is approximately:
#61. For repeated poles at s = -a (order 2), the time domain term includes:
#62. For a low-pass filter, the bandwidth is defined as the frequency where magnitude drops to:
#63. A lag compensator has a transfer function of the form:
#64. A second-order system has complex conjugate poles at s = -2 ± j4. The damping ratio ζ is:
#65. A marginally stable system has poles located:
#66. The transfer function H(s) = (s+2)/(s²+3s+2) simplifies to:
#67. A system with transfer function H(s) = 1/(s+1) is classified as:
#68. Partial fraction expansion is used to:
#69. The response of a linear system to input x₁(t) + x₂(t) is:
#70. A minimum phase system has:
#71. The inverse Laplace transform of F(s) = 1/(s+2) is:
#72. For a series RLC circuit with R=10Ω, L=1mH, C=1µF, the resonant frequency is:
#73. The transfer function of a pure gain K is:
#74. The 3-dB bandwidth of a first-order low-pass filter with τ = 1ms is:
#75. The phase shift of a first-order all-pass filter varies from:
#76. For a second-order system, the damped natural frequency ωd is related to ωn by:
#77. A system with transfer function H(s) = s/(s+1) is classified as:
#78. The frequency response magnitude |H(jω)| at very high frequencies for H(s) = s/(s+1) approaches:
#79. A series RLC circuit exhibits resonance when:
#80. The convolution of f(t) and g(t) in time domain corresponds to _____ in s-domain:
#81. The natural response of a system is determined by:
#82. Scaling the input by factor α scales the output by:
#83. The quality factor Q of a series RLC circuit is defined as:
#84. The initial value theorem states that f(0⁺) equals:
#85. The unit impulse response h(t) of a system equals:
#86. A system with H(s) = 1/s is called:
#87. The Laplace transform of the unit step function u(t) is:
#88. For F(s) = 1/(s(s+2)), using partial fractions, A in A/s + B/(s+2) equals:
#89. The Laplace transform of e^(-at)u(t) is:
#90. A system with poles in the right half of s-plane is:
#91. The unit step response of a first-order system 1/(1+sT) at t=T is:
#92. For a second-order system, critical damping occurs when ζ equals:
#93. The bandwidth of a first-order system with time constant T is:
#94. Convolution in time domain corresponds to _____ in frequency domain:
#95. The Laplace transform of tu(t) is:
#96. A system with H(s) = 1/(s²+2s+1) has damping ratio:
#97. The final value of response for H(s)=10/(s+2) with unit step input is:
#98. Rise time of a system is the time to go from:
#99. The natural frequency ωn of system 25/(s²+6s+25) is:
#100. For series RLC circuit, the damping ratio α equals:
