Question

Example 2 Find the impulse response function $h(t)$ to a linear engineering system modelled by the differential equation $\frac{d^2y}{dt^2} + 4y = e^{-t}$ $y(0) = 0$ and $y'(0) = 0$ Hence solve the system. Solution not given $y'' + y' + 4y - e^{-t} = 0$ $y'' + 4y - e^{-t} = 0$ $y''$ means double differential eg $(\frac{d^2y}{dt^2})$ Answer

Name: example 2 find the impulse response function ht to a linear engineering system modelled by the differential equation fracd2ydt2 4y e t y0 0 and y0 0 hence solve the system solution not given 29461
Uploaded: 2023-08-27T14:49:23-08:00
Channel: Victor Salazar
Description: example 2 find the impulse response function ht to a linear engineering system modelled by the differential equation fracd2ydt2 4y e t y0 0 and y0 0 hence solve the system solution not given 29461

          Example 2
Find the impulse response function $h(t)$ to a linear
engineering system modelled by the differential equation
$\frac{d^2y}{dt^2} + 4y = e^{-t}$
$y(0) = 0$
and $y'(0) = 0$
Hence solve the system.
Solution not given
$y'' + y' + 4y - e^{-t} = 0$
$y'' + 4y - e^{-t} = 0$
$y''$ means double
differential
eg $(\frac{d^2y}{dt^2})$
Answer

$example 2 find the impulse response function ht to a linear engineering system modelled by the differential equation fracd2ydt2 4y e t y0 0 and y0 0 hence solve the system solution not given 29461$

Added by Linda W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Victor Salazar

08/27/2023

Step 1

This is a second-order linear non-homogeneous differential equation. We can solve it using the method of undetermined coefficients. Show more…

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Example 2 Find the impulse response function $h(t)$ to a linear engineering system modelled by the differential equation $\frac{d^2y}{dt^2} + 4y = e^{-t}$ $y(0) = 0$ and $y'(0) = 0$ Hence solve the system. Solution not given $y'' + y' + 4y - e^{-t} = 0$ $y'' + 4y - e^{-t} = 0$ $y''$ means double differential eg $(\frac{d^2y}{dt^2})$ Answer