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crom1

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## Homework Statement

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)

## 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