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In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are...
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform...
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform (s2 +58 +6)Ý(s) = (s + 2) + (25+5)F(s) where f(s) = What is the zero-input response yzı(t)? yzi(t) = What is the zero-state response yzs(t)? yzs(t) = — What is the output signal y(t)? (t) =.
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1)...
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2 -40 -60 o-45 2 -90 O-135 -180 10 10 10 Frequency (rad/s) Find the steady state response of the system y$s (t), results from the sinusoidal input as: u(t) -2 sin(3t) Find the steady state response of the system yss (t), results from the sinusoidal input as: u(t) - 5 sin(10t) a) b) c) Find the input u(t) that results into a sinusoidal steady...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system.
5- For the following system: x(
Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
A linear, time-invariant system is modeled by the ordinary differential equation y(t) + 7y(t) = 14f(t)...
A linear, time-invariant system is modeled by the ordinary
differential equation
y(t) + 7y(t) = 14f(t)
Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1.
(a) Find the transfer function of the system and place your
answer in the standard form
H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 +
... + a1s + a0
(b) Determine the output of the system as
Y(s) = Yzs(s) + Yzi(s)
and place both the zero...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) +...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform (s2 +58 +6)Ý(s) = (s + 2) + (25+5)F(s) where f(s) = What is the zero-input response yzı(t)? yzi(t) = What is the zero-state response yzs(t)? yzs(t) = — What is the output signal y(t)? (t) =.
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
The Bode diagram below relates the input u(t) to the output y(t): Bode Diagram 20 2 -40 -60 o-45 2 -90 O-135 -180 10 10 10 Frequency (rad/s) Find the steady state response of the system y$s (t), results from the sinusoidal input as: u(t) -2 sin(3t) Find the steady state response of the system yss (t), results from the sinusoidal input as: u(t) - 5 sin(10t) a) b) c) Find the input u(t) that results into a sinusoidal steady...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system.
5- For the following system: x(
Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
A linear, time-invariant system is modeled by the ordinary
differential equation
y(t) + 7y(t) = 14f(t)
Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1.
(a) Find the transfer function of the system and place your
answer in the standard form
H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 +
... + a1s + a0
(b) Determine the output of the system as
Y(s) = Yzs(s) + Yzi(s)
and place both the zero...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
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