Ecet345 signals and systems homework #2

                                                ECET345 Signals and Systems

                                                                                Homework #2

Name of Student _____________________________________


1.       Redraw the following schematics with the impedance of each of the element shown in Laplace domain. Then determine the overall impedance of the entire circuit between the two ends of the shown circuit and express it in Laplace domain as a ratio of two polynomials in s, with the coefficients of the highest power if s in the numerator and denominator are made unity. (Follow the method outlined in the lecture to determine the impedances of elements in Laplace domain and then use the formulas for combining impedances in series and parallel.)










2.        (a) Apply Laplace transform to the following differential equation and express it as an algebraic equation in s.



(b) Given that all initial conditions are zero, (, solve for  as a function of time by inverting x(s) using Laplace transform pair tables. Show the steps you took in finding the answer.


Hint: Make use of the following Laplace transform pairs in this and following problems.



(c) Now solve the differential equation using the “Dsolve” command of MATLAB as explained in the lecture for Week 2. Paste your MATLAB commands and answers obtained below and prove that the two answers (one obtained by inverting using Laplace tables in part (b) and the answer provided by MATLAB) agree by solving for value of x(t) at t = infinity and t = 0 seconds in both cases. This shows that the same expression can be represented in more than one form. Trigonometric identities can be used to show that the two expressions are the same, though you are not required to do that as part of the homework.


3.       An RC circuit with an initial condition is shown below. The toggle switch is closed at t = 0. Assuming that a current i(t) flows clockwise in the circuit, Write the integral equation that governs the behavior of the circuit current and solve it for the current in the circuit i(t) and voltage across the capacitor as a function of time using Laplace transforms. Note the polarity of the initial condition as marked in the figure. (Take help from the document “Solving RC, RLC, and RL Circuits Using Laplace Transforms” (located in Doc Sharing) and the Week 2 Lecture to see how initial conditions are entered in Laplace domain.)



4.       The voltage in a circuit, expressed in Laplace domain, is given by the questions below.


a.       V(s) =  Find v(t) by first performing a partial fraction expansion and then inverting back to time domain using Laplace tables.






b.      Determine the numerical value of v(t) at t = 1 second.



c.       The voltage in a circuit, expressed in Laplace domain, is given by

V(s) =  . Find v(t) using Laplace tables.



d.      Determine the numerical value of v(t) at t = 1 second.


5.       An RLC circuit is shown below. There is an initial voltage of 5 V on the capacitor, with polarity as marked in the circuit. The switch is closed at t = 0 and a current i(t) is assumed to flow clockwise. Write the integral-differential equation of this circuit using Kirchoff’s method (sum of all voltages around a loop is zero). Apply Laplace transform as outlined in the lecture for Week 2 and in the document “Solving RC, RLC, and RL Circuits Using Laplace Transforms” (located in Doc Sharing) and write i(s) in Laplace transform notation. Express the denominator with the coefficient of the highest power of s unity. Then invert to obtain the current in time domain, i(t).






Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
The price is based on these factors:
Academic level
Number of pages
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

STAY HOME, SAVE LIVES. Order your essay today and save 20% with the discount code ATOM