Question

1. (50 points) A system is described by the following differential equation. $\frac{d^2y(t)}{dt^2} + 4\frac{dy(t)}{dt} + 13y(t) = \frac{dx(t)}{dt} + 3x(t)$ (a) Find the frequency response of the system. (b) Find the impulse response of this system. (c) For the two input signals $x_1(t)$ (whose Fourier transforms is given below), and $x_2(t)$ find the system outputs $y_1(t)$ and $y_2(t)$. 1. $X_1(j\omega) = \delta(\omega - 2) + 2\delta(\omega)$. ii. $x_2(t) = e^{-3t}u(t)$.

          1. (50 points) A system is described by the following differential equation.
$\frac{d^2y(t)}{dt^2} + 4\frac{dy(t)}{dt} + 13y(t) = \frac{dx(t)}{dt} + 3x(t)$
(a) Find the frequency response of the system.
(b) Find the impulse response of this system.
(c) For the two input signals $x_1(t)$ (whose Fourier transforms is given below), and
$x_2(t)$ find the system outputs $y_1(t)$ and $y_2(t)$.
1. $X_1(j\omega) = \delta(\omega - 2) + 2\delta(\omega)$.
ii. $x_2(t) = e^{-3t}u(t)$.

Show more…

1. (50 points) A system is described by the following differential equation.
(d^2y(t))/(dt^2) + 4(dy(t))/(dt) + 13y(t) = (dx(t))/(dt) + 3x(t)
(a) Find the frequency response of the system.
(b) Find the impulse response of this system.
(c) For the two input signals x1(t) (whose Fourier transforms is given below), and
x2(t) find the system outputs y1(t) and y2(t).
1. X1(jω) = δ(ω - 2) + 2δ(ω).
ii. x2(t) = e^-3tu(t).

Added by Ronald J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ameer Said

Step 1

The equation is: ii.xt=e-3tut Taking the Laplace transform of both sides, we get: sY(s) - y(0) + 3sX(s) - 3x(0) = 1/s^2 where Y(s) and X(s) are the Laplace transforms of yt and xt respectively, and y(0) and x(0) are the initial conditions. Since the initial Show more…

Show all steps

lock

Thanks for your feedback!

ii.xt=e-3tut i.Xjw=8(w-2+28w tfind the system outputs yt and yt. bFind the impulse response of this system. aFind the frequency response of the system. dt2 dt dy(t (c For the two input signals rtwhose Fourier transforms is given below, and +13y= 1. 50 points A system is described by the following differential equation. dt +3x dxt

Play audio

Feedback

Powered by NumerAI

Ameer Said and 93 other subject Physics 102 Electricity and Magnetism educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later