Question

Consider the third order LTI system:

ÿ(t)-5ÿ(t)+6ý(t)-2y(t)=3f`(t)-2f(t), t>0
Assume, y(0⁻)=1, ý(0⁻)=0, ÿ(0⁻)=0 and f(t)=e⁻ᵗu(t).
Solve for h(t),yₛₜₑₚ(t),yₛ(t) and yᵢ(t). Employ the Laplace transform method

Answer 1

The solution involves applying the Laplace transform method to obtain the various system responses of a third order LTI system, but key details are missing for a complete solution.

Step-by-step explanation:

The question pertains to solving for the impulse response h(t), the step response ystep(t), the forced response ys(t), and the natural response yi(t) of a third order LTI (Linear Time-Invariant) system using the Laplace transform method. Given the differential equation ÿ(t)-5ûe(t)+6ûe(t)-2y(t)=3f’(t)-2f(t) with initial conditions y(0⁻)=1, ûe(0⁻)=0, ÿ(0⁻)=0, and a forcing function f(t)=e⁻¹u(t), we would typically take the Laplace transform of both sides of the equation, apply the initial conditions, and solve for Y(s), which is the Laplace transform of y(t). Subsequently, the inverse Laplace transform would be used to obtain y(t). However, key details are missing for a full solution, such as the precise definitions of ys(t) and yi(t) in the context provided.