Question

Given the transfer function below, compute the system output for input u(t)=30.2cos(20t) G(s)= 2.4/ 0.6s²+8s+36

Answer 1

To compute the system output, find the Laplace transform of the input function and substitute it into the transfer function. Then, calculate the system output by multiplying the Laplace transforms and simplify the expression. Finally, take the inverse Laplace transform to get the system output.

Step-by-step explanation:

To compute the system output, we need to find the Laplace transform of the input function u(t) and substitute it into the transfer function G(s). The Laplace transform of u(t) is U(s).

U(s) = 30.2 / (s^2 + 20^2)

Now, we can calculate the system output Y(s) by multiplying U(s) with G(s) and simplify the expression.

Y(s) = U(s) * G(s) = 30.2 * (2.4 / (0.6s^2 + 8s + 36)) = (72.48 / (0.6s^2 + 8s + 36))

Finally, we can take the inverse Laplace transform of Y(s) to get the system output y(t).