ECE 421 - Fall 2021
Homework 1
Due Monday, Sep. 13
1. Obtain the Laplace transform of the following functions
(A)
(
f (t) =
0
t cos t
for t < 0
for t ≥ 0
(B)
(
0
e−0.5t sin 2t
for t < 0
for t ≥ 0
(
0
sin(t + π4 )
for t < 0
for t ≥ 0
f (t) =
(C)
f (t) =
2. Based on the finial-value theorem, find the steady state of a function f (t), whose Laplace
transform is given by
F (s) =
3. Find the transfer function F (s) =
5
s(s + 8)
U (s)
for the following electric system.
Y (s)
where u(t) is the input voltage, y(t) is the output voltage.
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Student Name:
θ2 (s)
θ1 (s)
and F2 (s) =
for the following mechanical
4. Find the transfer functions F1 (s) =
F (s)
F (s)
system, respectively
where T (t) is the input torque, θ1 (t) is the output angle for the first function, and θ2 (t)
is the output angle for the second function. (Hint. Use free-body diagrams on J1 and J2
respectively to obtain two equations. For F1 (s), try to cancel out θ2 ; For F2 (s), try to cancel
out θ1 .)
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