How do you determine if a differential equation is linear and time invariant

Q: Plot the following signals: 1. (a) y(t) = f 8(x)dx (b) 92 (t) = f(x-t)dx (c) ys(t)= (t(u(t)-…

A:

Q: 7. A pendulum moves with simple harmonic motion according to the equation: 0"+ 160= 0, where 0 is…

A: The Laplace Transform is a method for simplifying complicated differential equations by using…

Q: Question #7) Given x(t) = u(t) - u(t-1) and h(t) = t(u(t) - u(t-3)). The signal x(t) is sent as an…

A: Given: signalswe need to find and sketch: the output y(t) of a system having impulse response h(t)…

Q: 1 -In your own words and no more than three lines, explain the main difference(s) between Gauss's…

A: Difference  between Gauss's law and other integral differential equations are:

Q: y"+y' - 2y = 3cos3x - 11sin3x, given y(0) = 0 and y' (0) = 6 %3D %3D %3D

A:

Q: e(t) u(t) y(t) Controller Plant The controller and the plant are given as: d'y dy dt du + 3- + Y =…

A:

Q: Express the signals shown in terms of unit step functions

A: Step 1: Step 2: Step 3: Step 4:

Q: Simplify the given function using K-Map. Y (A, B, C, D) =Em (0,2,4,7,8,10,12) +d (5,6,13,14)

A: In this question we need to simplify the given Boolean function.

Q: find the expression i(t) with the help of the Residue Method. (Note: Do not use the Algebraic…

A: Given Data:A system of,To Find:The expression of i(t)

Q: v(t) t 1 2 3 4 2.

A:

Q: Given the graphical definitions of a function in the figure, graph the indicated transformations.…

A:

Q: For the give signal x2[n] below: п x2[n] = 2"u[n] + u[n] (i) Determine the z-transform and its…

A:

Q: K-Map. 1. Simplify the following function using F (A, B, C, D) {m (0_2,3,5,6,8,9 10,12,14,15)

A: The solution can be achieved as follows.

Q: Given the following K-map of the function g (a, b, c, d), where X is a don't-care: ab 00 01 11 00 1…

A:

Q: Problem # 11 Find the output y(t) for the system of Problem #9, Assume x1(0) =5, x2(0) =2 and…

A:

Q: 1. g(t) = [rect().t]+u(t-1)-u(t - 2) a) (15p) Graph g(t) b) (15p) Graph -2g (+)

A:

Q: the differential equation of a system is shown below B((d^2y)/(dt^2)+C(dy/dt)+Dy=B((d^2x)/(dt^2))…

A: Using laplace transform find input and output relation and than transfer function.  From the…

Q: By applying Kirchhoffs voltage law to a circuit, the following second order differential equation is…

A: Given that differential equations as  d²i/dt² +9i =18 given the initial conditions  i(0)=0 and di/dt…

Q: 3. Design and implement the given function using K-Map :- F = TtM (0,1,3,4,5,7,8,10,12,14) +…

A: Given, F=πM0,1,3,4,5,7,8,10,12,'4+d11,15…

Q: ix) f(t) = 8t“ + 2cos2t %3D f(t) = 4 + 9t° e³t f(t) = 4e 5t + e3t + 5 t³- 9 х) xi) %3D

A: As per our guidelines, we are supposed to answer only first 3 sub parts question. Kindly repost…

Q: Calculate the function given by using Laplace Transform Table. i) f(t) = 7e2 sin6t + 4eSt ii) f(t) =…

A:

Q: g(t) 12345 6

A:

Q: (ii) Determine the Inverse Laplace transformation of the following function. 6(s+2) F(s)…

A:

Q: Worte, but do not solve, the laplave transformor of the equations of motion for the shown below.…

A: Laplace transform is a method used by various electrical engineers to solve the typical mathematical…

Q: if 0 ≤ x ≤ 2 4-t if 2 ≤ x ≤4 = 2(u(t)-u(t-1))

A:

Q: 1. Find the Z-transform of the following functions, using the definition of the Z-transform. Your…

A:

Q: Q2 (a) Determine the inverse Laplace transform of X(s) : 9s2+16 (b) Produce the Inverse Laplace…

A: Use inverse transform table of Laplace By taking them to standard forms

Q: 4. In this problem, we will utilize the unit step function to express and different signals. (a)…

A:

Q: Write an expression for x 2(t+1) in terms of unit step function X2 3 1 3 4 Select one: O a.…

A:

Q: d*y(1) dy(f) + 4 dt + y(t) = 5r(t) , dt

A: Dear student as per our guidelines we are supposed to solve only one question.kindly repost other…

Q: 6] Use Laplace transforms to find an expression for current as a function of time in the following…

A:

Q: a) Read the following signal f(t), (write out the equation using a combination of unit-step and ramp…

A: Write the definitions of unit step and unit ramp functions.

Q: SITUATION STATEMENT: (Just read the situation, the question is at the bottom part of the problem)…

A: The given transfer function is Gs=YsRs, YsRs=s+cs2+as+bs+d. We need to determine the state space…

Q: Which of the following statements about Laplace transformations are true? Select one or more: O a.…

A: a. Reverse Laplace transformation means moving from the Laplace domain to the time domain. The…

Q: The following is known about x[n] and its z-transform X(z): x[n] is a real-valued, positive-time…

A:

Q: A system is described by the following differential equation, where X(t) is the input and y(t) is…

A:

Q: R(s) V₁(s) Vo(s) G₁(s) H(s) V₂(3)+ Vy(x) Vy(x) G₂(s) H₂(x) Va(s): Vs(s) (8) A Gy(s) Hy(s) C(s)

A: Given Data: A block diagram representation of the system with, Reference input=Rs Controlled Output…

Q: the differential equation when y(0) = 0, y'(0) = 10 %3D 5 + 6y = 12 dt

A:

Q: %3D Solve y" (t) – 5y' (t) – by(t) = 18t² + 12e2* ; y (0) = y' (0) = 0

A:

Q: Convolution in time domain is multiplication in Z-domain Z[x, (n) * x₂ (n)] = X₁ (z.) X₂ (z)…

A:

Q: 12 V R₁ ww C Data: C = ²F; R₁ = R₂= 6 N R₂ The switch is open for a long time before t = 0. At t= 0,…

A:

Q: #₁(t) = t -2 Define mathematical expression for each , (t) where i = 1, 2, 3 using the elementary…

A: We need to represent the given signal with respect to reference Signal.

Q: - Given x₁(t) = u(t) – u(t – 5); x2(t) = u(t − 2) — u(t − 4); x3(t) = e−³tu(t); x4(t) = e-¹tu(t),…

A: As per the honor code we can solve only 3 subparts at a time. Please repost your question to get the…

Q: Find a simplified expression for F (the inverse of F) using DeMorgan's Theorem. You will likely need…

A:

Q: 3. A linear time invariant system is given the input r₁(t) = e-4tu(t-1) and the output is observed…

A: