Homework Answers
Add Answer to:
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4....
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
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...
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 +...
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system 2. Consider a linear time-invariant system with transfer f...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation...
Find a first-order system of ordinary differential equations
equivalent to the second-order nonlinear ordinary differential
equation y ^-- = 3y 0 + (y 3 − y)
(3 points) Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y" = 3y' +(y3 – y).
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
4. [10 marks] A second order ordinary differential equation is defined on an interval [0,5) with...
4. [10 marks] A second order ordinary differential equation is defined on an interval [0,5) with boundary conditions, and is given as follows 2 + 3ty = 1+ cos(it), y(0) = 1, y(5) = 0 To solve the equation numerically we approximate it on a one-dimensional discrete mesh with N + 1 grid points. That is, we divide the interval (0,5) into subintervals of size h = 5/N and denote t; = ih, y(t) = y(ih)=yi, i = 0,1,... N...
3. a) Find a state space representation for a linear system represented by the following differen...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
solve all 22. The input-output relationship for a linear, time-invariant system is described by differential equation...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
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...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
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...
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
Find a first-order system of ordinary differential equations
equivalent to the second-order nonlinear ordinary differential
equation y ^-- = 3y 0 + (y 3 − y)
(3 points) Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y" = 3y' +(y3 – y).
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
4. [10 marks] A second order ordinary differential equation is defined on an interval [0,5) with boundary conditions, and is given as follows 2 + 3ty = 1+ cos(it), y(0) = 1, y(5) = 0 To solve the equation numerically we approximate it on a one-dimensional discrete mesh with N + 1 grid points. That is, we divide the interval (0,5) into subintervals of size h = 5/N and denote t; = ih, y(t) = y(ih)=yi, i = 0,1,... N...
3. a) Find a state space representation for a linear system represented by the following differential equation, where v(t) denotes the input and y(1) is the output: b) Consider a linear system represented by the following differential equation, where x() denotes the input and y(t) is the output: )+4()+4y()x(t) i) Write down its transfer function and frequency response function i) What is the form of the steady state response of the above system due to a periodic input that has...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
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...
Most questions answered within 3 hours.
-
The blues made its way into many kinds of music. Eric Clapton,
The Beatles, and Elvis...
asked 2 hours ago -
8. A wave in a string has a wave function given by: y (x, t) =...
asked 1 hour ago -
If you’re standing at the bottom of a hill and asked to evaluate
it while being...
asked 2 hours ago -
1. Which region has taken the lead in the world of
e-waste handling?
a) European Union...
asked 2 hours ago -
A 8.15- g bullet from a 9-mm pistol has a velocity of 366.0 m/s.
It strikes...
asked 4 hours ago -
The outstanding bonds of Alpha Extracts have a yield to maturity
of 7.4 percent and a...
asked 4 hours ago -
The Problem: The Case of the Harmonizing Vacations
Your CEO is exploring partnering with a European...
asked 5 hours ago -
A chemical equation is balanced by adding coefficients in front
of some formulas so that the...
asked 5 hours ago -
From the literature (reference your sources): What are the
lattice parameters of calcite and aragonite? Why...
asked 6 hours ago -
Your system is rejecting the question am asking which is
preceded by a case study. It...
asked 6 hours ago -
3. On January 2, 2000, Larry creates a trust with himself as
trustee. Larry as trustee...
asked 6 hours ago -
A member of the volleyball team spikes the ball. During this
process, she changes the velocity...
asked 6 hours ago