# Question 2.5: Simplify (−2 − j)^4.

Simplify $(−2 − j)^4$.

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Question: 2.27

## Initial Condition ≠ Initial Value Consider x + x + 2x = δ(t), x(0^-) = 0 where δ(t) denotes the unit-impulse. Recall that 0^- refers to the time immediately prior to t = 0 and x(0^-) is the  initial condition of x. Determine the initial values of x and x, that is, x(0^+) and x(0^+). ...

Taking the Laplace transform of the ODE and using ...
Question: 2.24

## Final-Value Theorem a. Find xss if X(s) = s+1/s(s² + 2s + 2) . b. Confirm in MATLAB. ...

a. The poles of $X(s)$ are at 0 and [...
Question: 2.23

## Initial-Value Problem Solve x + 3x + 2x = 0, x(0) = 0, x(0) = 1. ...

Taking the Laplace transform, s^{2}X(s)-s X...
Question: 2.22

## Initial-Value Problem a. Solve x + 4x = 2u(t), x(0) = 0, x(0) = 0, where u(t) is the unit-step function. b. Repeat in MATLAB. ...

a. Laplace transformation of the ODE (using Equati...
Question: 2.21

## Convolution Find L^-1{1/s²(s+1)}. ...

Let F(s)=\frac{1}{s^{2}(s+1)}=G(s) H(s)[/la...
Question: 2.17

## Linear Factors a. Find L^−1{X(s)} where X(s) = s+3/(s+1)(s+2). b. Verify in MATLAB. ...

a. $D(s)$ contains two linear factors...
Question: 2.13

## Integral of Laplace Transforms a. Find L {sinωt/t} t . b. Repeat in MATLAB. ...

a. Comparing with Equation 2.17, {\mathcal{...
Question: 2.12

## Derivative of Laplace Transforms a. Find L {te^−2t}. b. Repeat (a) in MATLAB. ...

a. Comparison with Equation 2.16 {\mathcal{...
Question: 2.9

## Second-Order ODE Solve x + ω²x = 0 (ω = const), x(0) = 0, x(0) = 1. ...

The characteristic equation \lambda^{2}+\om...
The characteristic equation, \lambda^{2}+3 ...