Consider a system characterized by the differential equation d²y(t) dy(t) +3 + 2y(t) = x(t). dt² dt (a) Determine the zero-state response of this system for the input x(t) = u(t). (b) Determine the zero-input response of the system for t > 0, given that y(0) 1, and dy(t) dt t=0- = 1. (c) Determine the output when the input is u(t) and the initial conditions are those of part (b).
Consider a system characterized by the differential equation d²y(t) dy(t) +3 + 2y(t) = x(t). dt² dt (a) Determine the zero-state response of this system for the input x(t) = u(t). (b) Determine the zero-input response of the system for t > 0, given that y(0) 1, and dy(t) dt t=0- = 1. (c) Determine the output when the input is u(t) and the initial conditions are those of part (b).
Introductory Circuit Analysis (13th Edition)
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Publisher:Robert L. Boylestad
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![Consider a system characterized by the differential equation
d²y(t) dy(t)
dt²
+3 + 2y(t) = x(t).
dt
(a) Determine the zero-state response of this system for the input x(t) = u(t).
(b) Determine the zero-input response of the system for t > 0, given that
y(0) = 1, and
dy(t)
dt It=0-
= 1.
(c) Determine the output when the input is u(t) and the initial conditions are those of part (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56658202-f4b1-4176-ad55-5e6ba5c24317%2F95993533-1f9f-4826-9ab4-02e6129491f8%2Ftgtxk3jy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a system characterized by the differential equation
d²y(t) dy(t)
dt²
+3 + 2y(t) = x(t).
dt
(a) Determine the zero-state response of this system for the input x(t) = u(t).
(b) Determine the zero-input response of the system for t > 0, given that
y(0) = 1, and
dy(t)
dt It=0-
= 1.
(c) Determine the output when the input is u(t) and the initial conditions are those of part (b).
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