Input output relationship of a continuous time linear time invariant system is represented oy a differential equation given as d²y(t) 4y(t) = x(t) dt2 where x(t) denotes the input while the output is denoted by y(t). The initial conditions are given as y(0) = 3 and dt =0 = 2. Find the output of this system when x(t) sin(2t) is applied as an input.

Input output relationship of a continuous time linear time invariant system is represented oy a differential equation given as d²y(t) 4y(t) = x(t) dt2 where x(t) denotes the input while the output is denoted by y(t). The initial conditions are given as y(0) = 3 and dt =0 = 2. Find the output of this system when x(t) sin(2t) is applied as an input.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Input output relationship of a continuous time linear time invariant system is represented
oy a differential equation given as
d²y(t)
dt2
where x(t) denotes the input while the output is denoted by y(t). The initial conditions are given as y(0) = 3
ay) -o = 2. Find the output of this system when x(t) sin(2t) is applied as an input.
4y(t) = x(t)
and
dt

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