Question

Consider the following initial value problem: $y'' + 4y' + 20y = \delta(t - \pi)$; $y(0) = 1$, $y'(0) = 0$ a) Find the solution $y(t)$. NOTE: Denote the Heaviside function by $u_c(t)$ where $u_c(t) = 1$ if $t \ge c$ and 0 otherwise. Indicate separately the exact value of c. $y(t) = $ where $c = $

Name: consider the following initial value problem y 4y 20y deltat pi y0 1 y0 0 a find the solution yt note denote the heaviside function by uct where uct 1 if t ge c and 0 otherwise indicate se 40213
Uploaded: 2024-12-04T13:09:42-08:00
Duration: 4 min 38 s
Channel: Shu Naito
Description: consider the following initial value problem y 4y 20y deltat pi y0 1 y0 0 a find the solution yt note denote the heaviside function by uct where uct 1 if t ge c and 0 otherwise indicate se 40213

          Consider the following initial value problem:
$y'' + 4y' + 20y = \delta(t - \pi)$; $y(0) = 1$, $y'(0) = 0$
a) Find the solution $y(t)$.
NOTE: Denote the Heaviside function by $u_c(t)$ where $u_c(t) = 1$ if $t \ge c$ and 0 otherwise. Indicate separately the exact value of c.
$y(t) = $
where $c = $

consider the following initial value problem y 4y 20y deltat pi y0 1 y0 0 a find the solution yt note denote the heaviside function by uct where uct 1 if t ge c and 0 otherwise indicate se 40213

Added by Melinda N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shu Naito

12/04/2024

Step 1

We will use the Laplace transform to solve this differential equation. Let $L\{y(t)\} = Y(s)$. The Laplace transform of the derivatives are: $L\{y'(t)\} = sY(s) - y(0)$ $L\{y''(t)\} = s^2Y(s) - sy(0) - y'(0)$ Substitute the initial conditions $y(0) = 1$ and Show more…

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Consider the following initial value problem: $y'' + 4y' + 20y = \delta(t - \pi)$; $y(0) = 1$, $y'(0) = 0$ a) Find the solution $y(t)$. NOTE: Denote the Heaviside function by $u_c(t)$ where $u_c(t) = 1$ if $t \ge c$ and 0 otherwise. Indicate separately the exact value of c. $y(t) = $ where $c = $