Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+...
Not yet graded /30 pts Question 3 A system is described by the following second-order linear differential equation dy + +5 6y(t)-4f(t )-3f(t) dt dt2 where y(0)-1. y (0) 5, and the input f(t) e'u(t) Solve the differential equation using the Laplace Transform method. Note that f(0) - 0 Your Answer: no option to upload answers so i emailed them to you Quiz Score: 0 out of 100 hp 12 144 5 6 Not yet graded /30 pts Question 3...
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.
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)...
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
please solve with steps and explain thanks Question 5 Given the differential equation y'' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(8) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Solve the following differential equation with given initial conditions using the Laplace transform. y" + 5y' + 6y = ut - 1) - 5(t - 2) with y(0) -2 and y'(0) = 5. 1 AB I
Relate to MATLAB and please do it by hand. Thanks 1. Given the following physical system described by the following differential equation. a. Solve for y(t), assume all initial conditions are zero. Use the Laplace transform approach. b. What MatLab command would you use to find the residues c. What is a residue? d. What command would you use to simulate and graph the step response? e. What is the purpose of the partial fractions operation? +12+3 32(0 dt dt...
6. Problem 6 Find the solutions in the time domain of the following second-order differential equation using the Laplace transform, (7a) (7b) (7c) y(0)-1; (0) =-1.
(b) A second-order differential equation is given as follows:$$ f^{\prime \prime}(t)-9 f(t)=g(t) $$where \(g(t)\) is a non-continuous function represented by,$$ g(t)=5 H(t)+H(t-1) $$Solve the differential equation using Laplace Transform, if the initial conditions are \(f(0)=0\) and \(f^{\prime}(0)=1\).