(a)
The value of
(a)
Answer to Problem 33E
The value of
Explanation of Solution
Given data:
The function is given as,
Calculation:
The function is simplified as,
Apply the partial fraction on the above expression.
The equation is written as,
Substitute
Substitute
The simplification of equation (3) is written as,
Equate the coefficient of
Substitute
Substitute
Substitute
The Laplace transform of
The Laplace transform of
The properties for Laplace transform are written as,
The inverse Laplace of the given function is written as,
Substitute
Conclusion:
Therefore, the value of
(b)
The value of
(b)
Answer to Problem 33E
The value of
Explanation of Solution
Given data:
The function is given as,
Calculation:
The function is simplified as,
Apply the partial fraction on the above expression.
The equation is written as,
Substitute
Substitute
The simplification of equation (8) is written as,
Equate the coefficient of
Substitute
Substitute
Substitute
The Laplace transform of
Substitute
Conclusion:
Therefore, the value of
(c)
The value of
(c)
Answer to Problem 33E
The value of
Explanation of Solution
Given data:
The function is given as,
Calculation:
The function is simplified as,
The Laplace transform of
Substitute
Conclusion:
Therefore, the value of
(d)
The value of
(d)
Answer to Problem 33E
The value of
Explanation of Solution
Given data:
The function is given as,
Calculation:
Substitute
Conclusion:
Therefore, the value of
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Chapter 14 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
- Find the Root locus : C(s) (K(S+ 2)(S + 3) S(S + 1) %3D R(s) Find the Root locus : C(s) R(s) (S – 1)(s² + 4s – 7) K Find the Root locus : (S + 2) (s2 + 6s + 10) G(s)arrow_forwardFind the range of K for which the system shown here is stable. R(s) E(s) K(s + 1) C(s) s(s + 2)(s + 3) s+5arrow_forwardWith the transfer functions given below: (a) Find the functions maximum overshoot, Mp (b) Find the functions rise times, t, (C) Find the functions settling times, t, 40 G2 (s) %3D (s+1) (s2 + 4s + 40)' 120 G3 (s) = %3D (s+3) (s2 +4s + 40)' 20(s+2) (s+1) (s2 + 4s + 40)' 3040 (s2 +s+ 401) G4 (s) = G, (s) 401 %3D (s2+4s+40) (s2 + s+901) Do by hand by using the time-domain specifications and the effects of zeros and additional poles to justify your answers.arrow_forward
- The block diagram of a time-invariant, linear, continuous-time system is given below. X 1 (s) and X 2 (s) are the state variables of the system. U(s) is the input signal of the system, Y(s) is the output signal of the system . X7(S) 1 S+5 Y(S) U(S) S-2 X2(S) Transfer function of the system A s + Bs + C Y (s) G (s) = U (s) %3D D s + Es + F According to the form of C. What is the value of the parameter? Note : Write only the numerical value of the parameter. 3.arrow_forwardUse G (s) = C(O) R(a) to find the response, c(t) to an input, r(t) = u(t), a unit step, assuming zero initial conditions.arrow_forwardfind the value of k to get make the system stable. C(s) R(s) E(s) G1(s) H(s) K G,(s) = s(s + 11)(s + 19) H(s) =arrow_forward
- Find f(t) for each of the following functions. 320 a) F(s) = = s²(s + 8) A th 80(s + 3) b) F(s) = s(s + 2)²* 60(s + 5) c) F(s) = = (s+1)(s2 + 6s+25) 25(s + 4)² d) F(s) = s²(s + 5)²arrow_forwardBelow is the differential equation of a system. d df 2 (t) d dt == x₁ (t) = x₂(t) 704x₁(t) x₂(t) + 4u(t) y(t) = x₁(t) + x₂(t) The initial conditions of the system are given below. x₁ (0) = 5, x₂ (0) = 10 Find the Mason gain formula and the Y(s)/ U (s) transfer function by drawing a signal flow diagram.arrow_forwardExamples Consider the following transfer functions. • Draw the pole-zero map i) G(s) = s +3 ii) G(s) = - S s(s + 2) (s + 1)(s + 2)(s + 3) (s +3)² s²(s +1) ii) G(s) = iv) G(s) = %3D s(s? +10) s(s +10)arrow_forward
- Find the D.E of the system below, given that r(t) = +² et 4 (t), where u (+) is a step function. R (s) s² - +1 55+354 +25² +1 c(s)arrow_forwardLTI system (t) = 2u(t)+u(t) x(0) = 1, ż(0) = -1, u(0) = 0 Write this system in the form X (s) = G(s)U(s) + (find G(s),c(s), r(s)). c(s) r(s) If the input is u(t) = et for t≥ 0, use Laplace transforms to find r(t) for t≥ 0. Identify rh (t) and xp(t) in your answerarrow_forwardThe simplified block diagram for position servo mechanism used in the base of a robotic arm is illustrated in Figure Q4. Investigate whether each of this statement is correct or false by using root locus approach. Q4 (a) (i) The break-away point of the system is at –0.835. (ii) The jo-axis crossing of the system is at +j2.51 .arrow_forward
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