P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the equationdžy(t)+30.5dt2dy(t)+4y(t) = x(t),dt(a) Find the frequency response H(ju) =Yjw of this system.(b) Find the impulse response, h(t).(c) What is the response of this system h(t) to a new input to the system x(t) = e-tu(t)?(d) What is the response of this system h(t) to a new input to the system x(t) = e-(t-2)u(t - 2)?

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P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the equation d³y(t) + 4y(t) = x(t), 0.5 +3y dt2 dt (a) Find the frequency response H(jw) = Y(Jw of this system. X(ja) (b) Find the impulse response, h(t). (c) What is the response of this system h(t) to a new input to the system x(t) = e-lu(t)? %3D

P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the equation d³y(t) + 4y(t) = x(t), 0.5 +3y dt2 dt (a) Find the frequency response H(jw) = Y(Jw of this system. X(ja) (b) Find the impulse response, h(t). (c) What is the response of this system h(t) to a new input to the system x(t) = e-lu(t)? %3D

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

P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the equation
džy(t)
+3
0.5
dt2
dy(t)
+4y(t) = x(t),
dt
(a) Find the frequency response H(ju) =
Yjw of this system.
(b) Find the impulse response, h(t).
(c) What is the response of this system h(t) to a new input to the system x(t) = e-tu(t)?
(d) What is the response of this system h(t) to a new input to the system x(t) = e-(t-2)u(t - 2)?

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