member 731016
- Homework Statement
- Please see below
- Relevant Equations
- Please see below
For this problem,
I'm confused how,
![Handwritten-style typeset solution: f(t) = 1 - H(t - 10) for any t >= 0 highlighted in orange; Laplace transform equation s^2 Y(s) + 3s Y(s) + 2Y(s) = 1/s - e^(-10s)/s; and Y(s) = 1/(s(s^2+3s+2)) - e^(-10s)/(s(s^2+3s+2)); with inverse transform L^-1[U(s)e^(-as)] = H(t-a)u(t-a).](https://www.physicsforums.com/attachments/1717971790764-png.346712/ "1717971790764.png")
However, not sure how to go from here.
$$
f(t) = \begin{cases}
1 & \text{if } 0 \leq t < 10\\
0 & \text{if } t \geq 10
\end{cases}
$$
By definition Heavside function is,
$$
H(t - 10) = \begin{cases}
1 & \text{if } t < 10\\
0 & \text{if } t \geq 10
\end{cases}
1 - H(t - 10) = 1 - \begin{cases}
1 & \text{if } t < 10\\
0 & \text{if } t \geq 10
\end{cases}
$$
However, I don't know where to go from here. Does anybody please know?
Thanks for any help!
I'm confused how,
However, not sure how to go from here.
$$
f(t) = \begin{cases}
1 & \text{if } 0 \leq t < 10\\
0 & \text{if } t \geq 10
\end{cases}
$$
By definition Heavside function is,
$$
H(t - 10) = \begin{cases}
1 & \text{if } t < 10\\
0 & \text{if } t \geq 10
\end{cases}
1 - H(t - 10) = 1 - \begin{cases}
1 & \text{if } t < 10\\
0 & \text{if } t \geq 10
\end{cases}
$$
However, I don't know where to go from here. Does anybody please know?
Thanks for any help!