A little confused in Zero Input response

Click For Summary
SUMMARY

The discussion focuses on finding the zero input response of the differential equation (D-1)(D²+1)y(t)=(D²+2)f(t) with initial conditions y(0)=4, y'(0)=3, and y''(0)=3. The roots of the characteristic equation are identified as +1, j, and -j. The user expresses confusion regarding the application of complex roots, particularly the imaginary unit j, in solving the equation. A step-by-step explanation is requested to clarify the process of incorporating these roots into the solution.

PREREQUISITES
  • Understanding of differential equations and their solutions
  • Familiarity with the Laplace transform and its applications
  • Knowledge of complex numbers and their properties
  • Basic concepts of initial value problems in control systems
NEXT STEPS
  • Study the application of the Laplace transform in solving differential equations
  • Learn about the method of undetermined coefficients for non-homogeneous equations
  • Explore the use of complex roots in characteristic equations
  • Review initial value problem techniques in engineering mathematics
USEFUL FOR

Students and professionals in engineering, particularly those studying control systems, differential equations, and applied mathematics, will benefit from this discussion.

zee3b
Messages
7
Reaction score
0
Guys I know how to solve the simple ones but this one has complex roots
I have to find the zero input response

(D-1)(D2+1)y(t)=(D2+2)f(t)

y(0)=4 y'(0)=3 y''(0)=3

D2= D square. Y' = first derivative Y''= secondI know the roots are +1, j and -j

But I don't know how to solve or use the j's and their identity

I maybe wrong. If it wasn't for the square inside the parenthesis I would be able to solve it.

Any help would be appreciated. (step by step so i can understand it better) once again I know the whole concept but not the j's
 
Physics news on Phys.org
Any one? :(
 

Similar threads

When Does the Prime Ratio of Spiral Diagonals Drop Below 10%?
  • · Replies 5 ·
Replies
5
Views
2K
Sum of All Positive Integers n where d+n/d is Prime to 100M
  • · Replies 80 ·
3
Replies
80
Views
10K
Write MATLAB code to find Y bus for any bus system
  • · Replies 1 ·
Replies
1
Views
2K
Comp Sci Validating Braces Placement for Expression Evaluation
  • · Replies 10 ·
Replies
10
Views
2K
Engineering Step response and realiziability of a G(q) transfer function
  • · Replies 1 ·
Replies
1
Views
3K
Engineering Recursive implementation of an FIR Filter
  • · Replies 2 ·
Replies
2
Views
2K
Comp Sci What Do Fortran77 Subroutines LZHES and LZIT Do?
  • · Replies 1 ·
Replies
1
Views
2K
Using ODE45 on Matlab to Integrate A Problem
  • · Replies 1 ·
Replies
1
Views
2K
Determine a transfer function in the `s` domain and the response to a ramp input
  • · Replies 23 ·
Replies
23
Views
6K
Solving An IVP on Matlab with ODE 45 with different tolerances
  • · Replies 2 ·
Replies
2
Views
2K