Question

\documentclass{article} \usepackage{amsmath} \begin{document} (1) [10 points] Using Laplace transform, find $y(t)$ for the system given by the following differential equation: \begin{equation} \frac{d^2y(t)}{dt^2} + 2\frac{dy(t)}{dt} + 2y(t) = \frac{df(t)}{dt} \end{equation} where the input $f(t)$ is unit step function $u(t)$. \newline $\dot{y}(0) = 10$, $y(0) = 1$ \end{document}

          \documentclass{article}
\usepackage{amsmath}
\begin{document}
(1) [10 points] Using Laplace transform, find $y(t)$ for the system given by the following differential equation:
\begin{equation*}
\frac{d^2y(t)}{dt^2} + 2\frac{dy(t)}{dt} + 2y(t) = \frac{df(t)}{dt}
\end{equation*}
where the input $f(t)$ is unit step function $u(t)$. \newline $\dot{y}(0) = 10$, $y(0) = 1$
\end{document}

(1) [10 points] Using Laplace transform, find y(t) for the system given by the following differential equation:

(d^2y(t))/(dt^2) + 2(dy(t))/(dt) + 2y(t) = (df(t))/(dt)

where the input f(t) is unit step function u(t). ẏ(0) = 10, y(0) = 1

Added by Melissa C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Frank Deng

Step 1

First, let's find the Laplace transform of the given differential equation. Taking the Laplace transform of both sides, we have: s^2F(s) - sf(0) - f'(0) = 10sY(s) - 10y(0) - y'(0) - Y(s) + sY(s) Show more…

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