What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0? - Study24x7
Social learning Network
study24x7

Default error msg

Login

New to Study24x7 ? Join Now
Already have an account? Login
googlePlay app_img
Goraksha Dadhich
30 Mar 2019 11:01 AM study24x7 study24x7

What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

A

(-1)n-1 + (4)n-2

B

(-1)n+1 + (4)n+2

C

 (-1)n+1 + (4)n-2

D

None of the mentioned

Banking Railways UPSC Sciences
Like Comment | 1 Share
study24x7
Write a comment
  • geet sharma
    •  Given difference equation is y(n)-3y(n-1)-4y(n-2)=0—-(1)
    Let y(n)=λn
    Substituting y(n) in the given equation
    => λn – 3λn-1 – 4λn-2 = 0
    => λn-2(λ2 – 3λ – 4) = 0
    the roots of the above equation are λ=-1,4
    Therefore, general form of the solution of the homogenous equation is

    The zero-input response of the system can be calculated from the homogenous solution by evaluating the constants in the above equation, given the initial conditions y(-1) and y(-2).
    From the given equation (1)
    y(0)=3y(-1)+4y(-2)
    y(1)=3y(0)+4y(-1)
    =3[3y(-1)+4y(-2)]+4y(-1)
    =13y(-1)+12y(-2)
    From the equation (2)
    y(0)=C1+C2 and
    y(1)=C1(-1)+C2(4)=-C1+4C2
    By equating these two set of relations, we have
    C1+C2=3y(-1)+4y(-2)=15
    -C1+4C2=13y(-1)+12y(-2)=65
    On solving the above two equations we get C1=-1 and C2=16
    Therefore the zero-input response is Yzi(n) = (-1)n+1 + (4)n+2.

    See more

    Like
    Reply 30 Mar 2019 11:49 AM
    Related Questions
    500+   more Questions to answer

    Popular Courses

    Revision batch for Physics (12th cl... All Levels English By V PLUS U
    Reasoning Special by Parwez Sir for... All Levels हिन्दी By Reasoning special by Parwez Alam
    RRB NTPC Previous Year Papers with ... All Levels हिन्दी By Just Asking - Lets check your knowl...
    Nutrition, Therapeutics and Health ... All Levels English By Dr. V. Vijaya Lakshmi
    Online Free SSC Mock Tests All Levels English By Topline Coaching
    Average and Alligation for Bank PO ... All Levels हिन्दी By logicalangle
    RRB NTPC Mock Test Free 2020 in Hin... All Levels हिन्दी By Topline Coaching
    Soil and Water Conservation Enginee... All Levels English By Prof. Rajendra Singh
    English Special Course for SSC CGL,... All Levels English By Topline Coaching 999 1,499 33% off
    FREE MOCK TEST FOR SSC CGL All Levels English By SSC Preparation Strategies & Study ...
    Featured Courses
    Popular Pages

    Featured Courses

    Basic Crop Production Practices (BCPP) All Levels English By Prof. J. R. Yadav Dr. Vinod Kumar Dr. Sharwan Kuma...
    FREE
    5.0
    BESTSELLER
    Reasoning Special by Parwez Sir for all Government... All Levels हिन्दी By Reasoning special by Parwez Alam
    FREE
    5.0
    Issues in Bioethics (Video) All Levels English By Dr. Sreekumar Nellickappilly
    FREE
    5.0
    GS 300 : Crash Course for BPSC & UPPSC Mains & PT Intermediate Level हिन्दी By Observer IAS 13,000 5.0
    IBPS PO (PRE) English Special by Pooja Mam All Levels English By Topline Coaching
    FREE
    5.0
    RRB NTPC Previous Year Papers with keys - In Hindi All Levels हिन्दी By Just Asking - Lets check your knowledge
    FREE
    5.0
    Dairy and Food process and products technology All Levels English By Prof. Tridib Kumar Goswami
    FREE
    4.5
    BANKING AWARENESS PREMIUM COURSE All Levels English By RAU IAS COACHING 499 5.0
    RRB JE Biology course All Levels English By Ashok Meena
    FREE
    4.5
    Math Special Course for SSC CGL, CPO, GD All Levels हिन्दी By Topline Coaching 999 5.0

    Popular Pages

    SAT (Scholastic Assessment Test)

    18 followers

    Study24x7

    1218 followers

    Reasoning special by Parwez Alam

    148 followers

    Henry Harvin

    58 followers

    RAU IAS COACHING

    1609 followers

    Daily Current Affairs

    2082 followers

    CBSE Study Materials

    83 followers

    RRB 2020-21 (Railway Jobs)

    500 followers

    Results Alert

    747 followers

    Topline Coaching

    3608 followers

    Get the App

    Download the Study24x7 App, so you can connect and collaborate.

    study24x7
    study24x7
    Most Related Articles