Consider a system described by the following input-output relationship: where T and K are constant. (a) If the input signal is described by u(t) = u 0 (t) and the initial value of the output is y(0)=...

Consider a system described by the following input-output relationship:

where T and K are constant.

(a) If the input signal is described by u(t) = u₀(t) and the initial value of the output is y(0)= y₀, compute and plot the response of the system y(t) for t ∈ [0, ∞].

(b) If the input signal is described by u(t) = u₀(t−t₀) and the initial value of the output is y(t₀) = y₀, compute the response of the system y(t) for t ∈ [t₀, ∞].

(c) If the input signal is described by u(t) = δ (t−t₀) and the initial value of the output is y(t₀) = 0, compute the response of the system y(t) for t ∈ [t₀, ∞].