Problem 3 A system is described by the following differential equation: d²x dx +6+8x(t) = f(t) dt dt² Where f(t) is the input signal, and x(0)=1. Find the solution of this differential equation using Laplace Transform for the following case: 1- F(t) is an impulse response, 2- F(t) is the unit step signal.

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Problem 3
A system is described by the following differential equation:
dx
+6+8 x(t) = f(t)
dt
d²2x
dt²
Where f(t) is the
input signal, and x(0)=1.
Find the solution of this differential equation using Laplace
Transform for the following case:
1- F(t) is an impulse response,
2- F(t) is the unit step signal.
Transcribed Image Text:Problem 3 A system is described by the following differential equation: dx +6+8 x(t) = f(t) dt d²2x dt² Where f(t) is the input signal, and x(0)=1. Find the solution of this differential equation using Laplace Transform for the following case: 1- F(t) is an impulse response, 2- F(t) is the unit step signal.
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