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5) Consider the linear system described by the following differential equation: $x¨+2ax˙+(a_{2}+4)x=F(t)$ (Here $a>0$ is a constant parameter) (a) Find the transfer function $x(s)/F(s)$ (b) IF $F(t)=δ(t)$, $F∩ND×(t)$ (assuming zero initial conditions)

We are given a second-order linear differential equation with a forcing function on the right-hand side. To solve this equation, we will first find the transfer function of the system, which relates the Laplace transform of the output to the Laplace transform of the input.

Given Differential Equation;

(a) To find the transfer function, we need to take the Laplace transform of both sides of the differential equation with zero initial conditions: