Question

Use the transfer functions given below to find the steady-state response yₛₛ(t) to the given input function f(t),

a) T(s)=Y(s)/F(s) = 75 / 14s+18 , f(t)= 10 sin 1.5t
b) T(s)=Y(s)/F(s) = 5s / 3s+4 , f(t) = 15 sin 100t
c) T(s)=Y(s)/F(s) = s+50 / s+150 , f(t) = 15 sin 100t

Answer 1

To find the steady-state response yₛₛ(t) to the given input function f(t), we can use the Laplace transform. We can apply this process to each part of the question, using the transfer functions and input functions given.

Step-by-step explanation:

To find the steady-state response yₛₛ(t) to the given input function f(t) using the transfer functions, we can use the Laplace transform. The Laplace transform of a sine function is given by F(s) = 1 / (s^2 + ω^2), where s is the complex frequency and ω is the angular frequency.

For part a) with transfer function T(s) = 75 / (14s+18) and input function f(t) = 10sin(1.5t), the Laplace transform of the input function is F(s) = 10 / (s^2 + 2.25). To find the steady-state response, we can multiply the transfer function and the Laplace transform of the input function, which gives Y(s) = 10 / (2.25(14s+18)). Taking the inverse Laplace transform of Y(s) will give us the steady-state response yₛₛ(t).

Similarly, we can apply the same process for parts b) and c) with their respective transfer functions and input functions.