ax" + bæ' + cx = f(t), x(0) = 0, x'(0) = 0, for time 0 0. Find X(s) = L {æ(t)} and F(s) = L{f(t)}. X(s) = help (formulas) F(s) = help (formulas) Now find the system transfer function, H(s). H(s) help (formulas) What will be the output if a Heaviside unit step input f(t) = u(t) is applied to the system? New x(t) help (formulas)
ax" + bæ' + cx = f(t), x(0) = 0, x'(0) = 0, for time 0 0. Find X(s) = L {æ(t)} and F(s) = L{f(t)}. X(s) = help (formulas) F(s) = help (formulas) Now find the system transfer function, H(s). H(s) help (formulas) What will be the output if a Heaviside unit step input f(t) = u(t) is applied to the system? New x(t) help (formulas)
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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Transcribed Image Text:ax"
+ bæ' + cx = f(t), x(0) = 0, x'(0) = 0,
for time 0 <t < o0, where a, b, c are constants and f(t) is a known function. We view this problem as a linear system, where f(t) is a known input and the
solution x(t) is the output. Laplace transforms of the input and output functions satisfy the relation X(s) = H(s)F(s), where we call
X(s)
F(s)
1
H(s)
as? + bs + c
the system transfer function.
Suppose an input f(t) =
3t, when applied to the linear system above, produces the output æ(t) = 2(et – 1) + t(e+ 1), t > 0.
Find X(s)
L{x(t)} and F(s) = L {f(t)}.
X(s) =
help (formulas)
F(s) =
help (formulas)
Now find the system transfer function, H(s).
H(s) =
help (formulas)
What will be the output if a Heaviside unit step input ƒ(t)
u(t) is applied to the system?
New x(t) =
help (formulas)
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