QUESTION 4 B i. Consider the piecewise function ii. iii. 6t, 12, 0 ≤t <2, t≥ 2. f(t)= Express the function f(t) in terms of unit step function. Then, show that C{f(t)} 6 6e-28 S² 82 By using convolution theorem, determine 2 C-¹ { 3² (3²-1)} Hence, based on the results in part (i) and part (ii), use Laplace transform to solve the system of differential equations da = y+ dt f(t), dy 4x + HT 0, dt. given that x=y=0 when t = 0. T
QUESTION 4 B i. Consider the piecewise function ii. iii. 6t, 12, 0 ≤t <2, t≥ 2. f(t)= Express the function f(t) in terms of unit step function. Then, show that C{f(t)} 6 6e-28 S² 82 By using convolution theorem, determine 2 C-¹ { 3² (3²-1)} Hence, based on the results in part (i) and part (ii), use Laplace transform to solve the system of differential equations da = y+ dt f(t), dy 4x + HT 0, dt. given that x=y=0 when t = 0. T
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:QUESTION 4 B
i.
ii.
iii.
Consider the piecewise function
f(t) =
6t,
12,
Express the function f(t) in terms of unit step function. Then, show
that
C{f(t)}
By using convolution theorem, determine
C-¹ {3² (6²2²-1)}
y+
0 ≤t <2,
t≥ 2.
6 6e-28
s²
82
Hence, based on the results in part (i) and part (ii), use Laplace
transform to solve the system of differential equations
4x +
da
dt
dy
dt.
given that x=y=0 when t = 0.
f(t),
=1 0,
4
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