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We are examining the **“Electrical and Electronics Engineering”** unit 03, “**Laplace Transform Analysis,**” | “**Basic Signal and Systems assignment from AKTU**. I hope this article is useful to you as you prepare for your AKTU exams.

Dudes 🤔.. You want more useful details regarding this subject. Please keep in mind this as well.Important Questions For Basic Signals and Systems :*Unit-01 *Unit-02 *Unit-03 *Unit-04 *Unit-05 *Short-Q/Ans *Question-Paper with solution 21-22

**Q1. Calculate the Laplace transform for the function F(t) = e**^{-at}** sin hbt.**

^{-at}

**Ans. **

**Q2. Find the Laplace transform of signal u(t). **

**Ans. **

**Q3. What are the different properties of laplace transform ? **

**Ans. 1. Linearity:** Considering two signals x_{1}(t) and x_{2}(t) with Laplace transforms X_{1}(s) and X_{2}(s) respectively. ** **

**2. Time shifting: **

If the x(t) signal is delayed in time by t_{0} unit then its Laplace transform is multiplied by e^{-sto} factor.

**3. Frequency shifting:** If there is any shift in X(s) by a unit, it will cause a multiplication factor e^{at} in signal x(t).

**4. Differentiation theorem: **

**5. Differentiation by s: **In the time-domain, multiplying by t corresponds to differentiation in the complex frequency-domain.

**7. Scaling property:** This theorem states that,

**Q4. If the laplace transform of x(t) is (s + 2)/(s**^{2}** + 4s + 5), determine the laplace transform of y(t) = x(2t – 1) u(2t 1). **

^{2}

**Ans. **1. The Laplace transform of x(t) u(t) is

2. Applying time shifting property.

3. Now, applying time scaling property.

4 Hence, the Laplace transform of y(t) = x(2t – 1) u (2t – 1) is,

**Q5. A signal has Laplace transform X(s) **

**Find the Laplace transform Y(s) of the following signals **

**i. y(t) = tx(t)**

**ii. y(t)=e**^{-t}**x(t) **

**Ans. **

**Q6. Calculate the inverse Laplace transform of right-sided sequences with the following transfer functions:**

**Ans. **

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