Question

Problem 5: Given a system described by the transfer function $H(s) = \frac{Y(s)}{X(s)} = \frac{-5s+6}{s^2+4s+13}$ with initial conditions and input: $y(0^-) = 3$, $\frac{dy(t)}{dt}|_{t=0^-} = -2$, $x(t) = e^{-4t}u(t)$, where $y(t)$ is the output response and $x(t)$ is the input signal. Find $y(t)$ and steady-state output.

          Problem 5: Given a system described by the transfer function
$H(s) = \frac{Y(s)}{X(s)} = \frac{-5s+6}{s^2+4s+13}$
with initial conditions and input: $y(0^-) = 3$, $\frac{dy(t)}{dt}|_{t=0^-} = -2$, $x(t) = e^{-4t}u(t)$, where $y(t)$ is the output
response and $x(t)$ is the input signal. Find $y(t)$ and steady-state output.

Problem 5: Given a system described by the transfer function
H(s) = (Y(s))/(X(s)) = (-5s+6)/(s^2+4s+13)
with initial conditions and input: y(0^-) = 3, (dy(t))/(dt)|t=0^- = -2, x(t) = e^-4tu(t), where y(t) is the output
response and x(t) is the input signal. Find y(t) and steady-state output.

Added by Hannah K.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert C D

Step 1

The transfer function X(s) = -2e^(-4s) / (s^2 + 4s + 13) can be written as: X(s) = -2e^(-4s) / ((s+2)^2 + 9) To find the inverse Laplace transform, we need to rewrite the transfer function in a form that matches a known Laplace transform pair. In this case, we Show more…

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Problem 5: Given a system described by the transfer function X(s) = -2e^(-4s) / (s^2 + 4s + 13), where y(t) is the output response and x is the input signal. Find y and the steady-state output.