A continuous-time LTI system is described by the following differential equation d'y(t) , dy(t) dr(t) + 3y(t) : dt dt2 dt (a) Determine the homogeneous solution yh(t) (b) Determine the particular solution when x(t) 10 cos(V3t)u(t) (c) Determine the total solution y(t) when y(0) = 1 and dy(0) = 0 dt

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A continuous-time LTI system is described by the following differential equation
dy(t)
dy(t)
+ 3y(t) =
dx(t)
dt2
dt
dt
(a) Determine the homogeneous solution yh(t)
(b) Determine the particular solution when x(t) = 10 cos(/3t)u(t)
(c) Determine the total solution y(t) when y(0) = 1 and
dy(0)
= 0
dt
Transcribed Image Text:A continuous-time LTI system is described by the following differential equation dy(t) dy(t) + 3y(t) = dx(t) dt2 dt dt (a) Determine the homogeneous solution yh(t) (b) Determine the particular solution when x(t) = 10 cos(/3t)u(t) (c) Determine the total solution y(t) when y(0) = 1 and dy(0) = 0 dt
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