Don't use Laplace transform methods to solve this problem.
4- Determine the impulse response of the following differential equations +5 w d3wd2w dt di2
use the Laplace transform to solve the given system of differential equations dx dt dx dt dt dt x(0) 0, y(o)0 x(t) =
2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1
2. Using Laplace transform, solve the system of differential equations d.x: dy dt where x(0)1
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
Solve each of the following differential equations using the Laplace Transform approach and plot the response of the system to the given change in u(). (Linearize where necessary) dy ch + 2 t-0
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
Use Laplace Transform to solve the following Differential Equations
y - zsin (5+)=Y , Y'(o)=0 Y
(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...
Solve the system of differential equations using Laplace transformation dx dy dt - x = 0, + y = 1, x(0) = -1, y(0) = 1. dt You may use the attached Laplace Table (Click on here to open the table) Paragraph В І
Use the Laplace transform to solve the given system of
differential equations.
Use the Laplace transform to solve the given system of differential equations. of + x - x + y = 0 dx + dy + 2y = 0 x(0) = 0, y(0) = 1 Hint: You will need to complete the square and use the 1st translation theorem when solving this problem. x(t) = y(t) =