3a) A linear system is characterized by the following differential equation (below). If the input, f(t) = 1, were applied to this system at t = 0 and it was known that the output and its first derivative were 0 at t = 0, then find the complete response of the system for positive time. () + 5y(t) + 6y() = 6At) %3D 3b) In prob. 3a above, suppose y(0) = 2, and the derivative is still 0 at t = 0. Find the zero input response.

3a) A linear system is characterized by the following differential equation (below). If the input, f(t) = 1, were applied to this system at t = 0 and it was known that the output and its first derivative were 0 at t = 0, then find the complete response of the system for positive time. () + 5y(t) + 6y() = 6At) %3D 3b) In prob. 3a above, suppose y(0) = 2, and the derivative is still 0 at t = 0. Find the zero input response.

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

3a) A linear system is characterized by the following differential equation (below). If the input,
f(t) = 1, were applied to this system at t = 0 and it was known that the output and its first
derivative were 0 at t = 0, then find the complete response of the system for positive time.
j(t) + 5y(t) + 6y(t) = 6At)
3b) In prob. 3a above, suppose y(0) = 2, and the derivative is still 0 at t = 0. Find the zero input
response.

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