Homework Answers
Answer 9
According to final value theorem,
![\small \lim_{t\rightarrow \infty }f(t)=\lim_{s\rightarrow 0}[sF(s)]](http://img.homeworklib.com/questions/2c571480-028a-11eb-9fa3-6f388dd1cac0.png?x-oss-process=image/resize,w_560)
The conditions under which the final value theorem may not be used
1. The Poles of F(s) are in the right-half of s-plane.
2. F(s) has more than one pole at the origin.
3. The poles of F(s) lies on the imaginary axis.
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9. Define the conditions under which the final value theorem may NOT be used (i.e. gives...
11. We are given the following factored Laplace transform and wish to use the final value...
11. We are given the following factored Laplace transform and wish to use the final value theorem to determine the value of y(t) at infinity (s + 5) Y(s) s(s + 10)(S-1 Which of the following is the final value? 0 1 2 1 2 1 -1 infinity cannot use theorem Which of the following is the initial value? 0 1 2 1 -1 infinity cannot use theorem 2 12. The Laplace transform is a linear operator True False depends...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use b...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use block diagram reduction to obtain the transfer function YIR of the following feedback system. Fuc R(s) Manifold Air b Ga(a) G1) Pressure Sparks pai FIQUREdle soed cortenal aetem
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding...
How to prove this? Laplace transform If f(t) satisfies those conditions f(t) is even function which...
How to prove this? Laplace transform
If f(t) satisfies those conditions f(t) is even function which has the property of f(t) = f(-t) Laplace transform of f(t) is F(s) then Laplace transform of f(at) is F(s/lal)/lal for any non-zero constant a Prove this - How about odd function f(t) which has the property of f(-t) -f(t) ?
If f(t) satisfies those conditions f(t) is even function which has the property of f(t) = f(-t) Laplace transform of f(t) is F(s)...
Write the laplace transform of the following, assuming zero initial conditions, i.e f(0) 0 f (0) ...
Write the laplace transform of the following, assuming zero initial conditions, i.e f(0) 0 f (0) 0 Part D- Dynamic Systems1 Keep X(s) terms on the left and Y(s) terms on the right of the equation. Do not group your terms and write your final answer in the order of the equation given vec 5s +4s +6X(s) (s+6)Y(s) Submit Previous Answers Request Answer XIncorrect: Try Again The correct answer involves the function sX, which was not part of your answer....
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal...
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Signal and Systems Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response...
Signal and Systems
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...
you can do by hand Question 8: Compute the Laplace Transform Ts, then use the final value theorem to find the limiting t...
you can do by hand
Question 8: Compute the Laplace Transform Ts, then use the final value theorem to find the limiting temperature in each room after a long time. Use eye(3) for the 3x3 identity matrix I. Use inv() for the inverse matrix of the matrix. Declare s to be symbolic Name your result Ts. This is the solution for the model in the s-domain. l(T) = (sl-A)-1 T(0) +-. f >> Tinf vpa (limit (s*TS, 0), 4) =...
Question: given a differential equation: a. initial conditions for the plan and input are zero, ...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0)...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
Do: Find the Laplace transform, F(s), for each f(t) given below in parts a) and b). Express F(s) polynomials ins w...
Do: Find the Laplace transform, F(s), for each f(t) given below in parts a) and b). Express F(s) polynomials ins where the denominator polynomial, A(s) Le., it has the value "1" (one) Monic Rational Form (MRF). This means that the result is a ratio of polynomials, and the coefficient, a, in the denominator polynomial, A(s) below is a, 1 as a ratio of =s"+a-1s"- + a28 +a1s +a0, is monic as the leading coefficient on the highest power of s....
11. We are given the following factored Laplace transform and wish to use the final value theorem to determine the value of y(t) at infinity (s + 5) Y(s) s(s + 10)(S-1 Which of the following is the final value? 0 1 2 1 2 1 -1 infinity cannot use theorem Which of the following is the initial value? 0 1 2 1 -1 infinity cannot use theorem 2 12. The Laplace transform is a linear operator True False depends...
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding time function f(t) using partial fractions. a Use block diagram reduction to obtain the transfer function YIR of the following feedback system. Fuc R(s) Manifold Air b Ga(a) G1) Pressure Sparks pai FIQUREdle soed cortenal aetem
0.1.For the following Laplace transform, F(s) a) Determine the steady state solution fs using the Final value theorem. b) Find the corresponding...
How to prove this? Laplace transform
If f(t) satisfies those conditions f(t) is even function which has the property of f(t) = f(-t) Laplace transform of f(t) is F(s) then Laplace transform of f(at) is F(s/lal)/lal for any non-zero constant a Prove this - How about odd function f(t) which has the property of f(-t) -f(t) ?
If f(t) satisfies those conditions f(t) is even function which has the property of f(t) = f(-t) Laplace transform of f(t) is F(s)...
Write the laplace transform of the following, assuming zero initial conditions, i.e f(0) 0 f (0) 0 Part D- Dynamic Systems1 Keep X(s) terms on the left and Y(s) terms on the right of the equation. Do not group your terms and write your final answer in the order of the equation given vec 5s +4s +6X(s) (s+6)Y(s) Submit Previous Answers Request Answer XIncorrect: Try Again The correct answer involves the function sX, which was not part of your answer....
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Signal and Systems
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...
you can do by hand
Question 8: Compute the Laplace Transform Ts, then use the final value theorem to find the limiting temperature in each room after a long time. Use eye(3) for the 3x3 identity matrix I. Use inv() for the inverse matrix of the matrix. Declare s to be symbolic Name your result Ts. This is the solution for the model in the s-domain. l(T) = (sl-A)-1 T(0) +-. f >> Tinf vpa (limit (s*TS, 0), 4) =...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...
Do: Find the Laplace transform, F(s), for each f(t) given below in parts a) and b). Express F(s) polynomials ins where the denominator polynomial, A(s) Le., it has the value "1" (one) Monic Rational Form (MRF). This means that the result is a ratio of polynomials, and the coefficient, a, in the denominator polynomial, A(s) below is a, 1 as a ratio of =s"+a-1s"- + a28 +a1s +a0, is monic as the leading coefficient on the highest power of s....
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