1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Signals and systems problem

  1. Jun 21, 2017 #1
    1. The problem statement, all variables and given/known data
    continuous time LTI system is given with differential equation y'(t) + 5y(t) = 10u(t)
    a) Find transfer function of system and determine is it stable or not.
    b)Find frequency characteristics (amplitude and phase angle) of given system
    c) Find impulse response using Laplace transformation
    d) Find zero-input response(I think that's the right word) for u(t) = 6cos(5t)μ(t)

    3. The attempt at a solution
    Ok, I got
    a) Y(s) = 10/(s+5) * U(s) , pole is s=-5 , and Re(s)<0 so the system is stable
    b) Plug s=jω in H(s)=10/(s+5) , then |H(jω)| = 10/(√s^2+ω^2) and ∠H(jω) = - arctan(ω/5)
    c) for impulse response U(s) = 1, Y(s) = 10/(s+5) ⇒ y(t) = 10*e^(-5t) , t>0
    d) Using frequency characteristics, we have ω=5, and |H(j5)| = √2 and ∠H(j5) = -π/4 so the response is
    y(t) = 6√2 *cos(5t-pi/4)

    I need someone to say if these are correct or not, if not i will post my full attempt and reasoning. Thanks
     
  2. jcsd
  3. Jun 24, 2017 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    10 U(s) is not part of the transfer function. It's a specific input; the transfer function gives output for any input.
    OK but leave out the "10". Also, typo used "s" for "5".
    U is a step function.The symbol for impulse input is δ(t). Your actual input is kδ(t), k = 1 volt-sec. Careful with δ(t), its units are time-1. Again, ditch the "10".
    never heard of "zero input response". You mean mean input is 6cos(5t)U(t) or ??? Never saw μ(t) either.
    Strange they never asked for the time response to the 10u(t) input ...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted