Laplace Transform method,
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- Why we would want to use the Laplace transform. When can we employ it (think about conditions), and why is it beneficial? Please answer in detail with good reasons and type your answer. Do not copy..The Laplace Transform can be used to solve differential equations using a four step process. 1.Take the Laplace Transform of the differential equation using the derivative property (and, perhaps, others) as necessary.2.Put initial conditions into the resulting equation.3.Solve for the output variable.4.Get result from Laplace Transform tables which in the picture. If the result is in a form that is not in the tables, you'll need to use the Inverse Laplace Transform. Solve the following DE using Laplace Transform Method:1. f(x) = e-2x (1-2x)a) Based on your understanding, describe the use of Laplace-transform and z-transform in linear time invariant analysis.b) Find Laplace transform and sketch the associated ROC of following function,i. ?(?)=(?+1)?−??(?)ii. ?(?)=?−2?[?(?)−?(?−4)].c) Find z-transform and sketch the associated ROC of following function,i) ?[?]=(23)??[?]+(16)??[?]ii) ?[?]=?3??[?]
- Find the initial and final values of the current ?0(?) in the circuit in Figure 2 using the Laplace transform?The signal shown in Figure 3(b) is applied to the circuit shown in Figure 3(a) as the input voltage ??(?). Find the output voltage value ?0(?) in the circuit in Figure 3(a) using the Laplace transform?1. Explain in not less than 7 sentences with mathematical equations the relationship of z-transform and convolution sum. 2.Some transforms in the z-transform pairs are exactly the same. How would did they differ in other parts? What would be its implication when solving z-transforms?
- Taking the inverse Laplace transform gives us a function that is in the time domain. Select one: True False The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero. Select one: True False L(f(t)/t) = -F’(s). Select one: True False If the denominator of a Laplace transform has degree 4, you should expect to find 4 items in the table to use for writing the transform as a sum of terms. Select one: True False Laplace transform is a linear operator. Select one: True False The Laplace transform of two functions is equal. The functions are equal. Select one: True False Daniel Bernoulli is the original author of Laplace Transform. Select one: True False Inverse Laplace transform is a linear operator. Select one: True False L(f*g) = L(f).L(g). Select one: True False The Laplace transform of the sum of two functions is equal to the sum of…In the given circuit, where R = 1 ohm and and L=1H, solve for i(t) using the Laplace Transform. The time-domain current source is(t) is given in the plot below. a) Draw the circuit’s s-domain (for Laplace transform) equivalent. b) Using Laplace Transform to find the solution.Use the concepts of Laplace Transform, Transform of the Derivative, and Inverse Laplace Transform to solve the following: A 30V electromotive force is applied to an LR-series circuit in which the inductance is 0.1H and the resistance is 50 ohms. Find the current i(t) if i(0) =0. Determine the current as t approaches infinity.
- Evaluate the inverse z-transform of of the functions given below by the three methods described in the text: E(z)=0.5z/(z-1)(z-0.6)I need help with the question below. 1. By the direct integration, i.e. using the formula of Laplace transform, find the Laplace transform of (i) 2u(t) − 2u(t − 1), (ii) te^−(2t)u(t).2. Also, state their region of convergence. 3. Sketch both of the signals.For each of the transfer functions shown below, findthe locations of the poles and zeros, plot them on thes-plane, and then write an expression for the generalform of the step response without solving for theinverse Laplace transform. State the nature of eachresponse (overdamped, underdamped, and so on).[Sections: 4.3, 4.4]