Recall that the sawtooth wave is the piecewise linear function defined by saw (t):= t- [t], where [t] is the largest integer not greater than t. See the sketch graph of saw (t) + below. Compute its Laplace transform, for t > 0. 1.6 14 1.2- 1.0- 0.8 0.6 0.4 02- 05 saw(t)+¹/2 15 t 2.5 3 3.5 Consider the spring/mass system defined by 1 2' y" + 3y = saw(t) + where y(0) = y'(0) = 0, and saw(t) is as defined in the part (a). Find a function that predicts the motion of the mass. Write your final answer as a piecewise function when 0 ≤ t ≤ 3.
Recall that the sawtooth wave is the piecewise linear function defined by saw (t):= t- [t], where [t] is the largest integer not greater than t. See the sketch graph of saw (t) + below. Compute its Laplace transform, for t > 0. 1.6 14 1.2- 1.0- 0.8 0.6 0.4 02- 05 saw(t)+¹/2 15 t 2.5 3 3.5 Consider the spring/mass system defined by 1 2' y" + 3y = saw(t) + where y(0) = y'(0) = 0, and saw(t) is as defined in the part (a). Find a function that predicts the motion of the mass. Write your final answer as a piecewise function when 0 ≤ t ≤ 3.
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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![Recall that the sawtooth wave is the piecewise linear function defined by saw (t):
t- [t], where [t] is the largest integer not greater than t. See the sketch graph of saw (t) + below.
Compute its Laplace transform, for t > 0.
18
16
14
1.2
1.0-
0.8-
0.6
0.4
0.2
0.5
I
saw(t) + 1/2
15
2
t
25
3
3.5
Consider the spring/mass system defined by
1
2'
where y(0) = y'(0) = 0,
and saw(t) is as defined in the part (a). Find a function that predicts the motion of the mass. Write
your final answer as a piecewise function when 0 < t <3.
y" + 3y = saw(t) +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf58e778-209d-4051-b758-0c57e3f8187c%2F45aa3339-0214-4932-a5fd-c4b3c9d197b9%2F5ta2nw6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Recall that the sawtooth wave is the piecewise linear function defined by saw (t):
t- [t], where [t] is the largest integer not greater than t. See the sketch graph of saw (t) + below.
Compute its Laplace transform, for t > 0.
18
16
14
1.2
1.0-
0.8-
0.6
0.4
0.2
0.5
I
saw(t) + 1/2
15
2
t
25
3
3.5
Consider the spring/mass system defined by
1
2'
where y(0) = y'(0) = 0,
and saw(t) is as defined in the part (a). Find a function that predicts the motion of the mass. Write
your final answer as a piecewise function when 0 < t <3.
y" + 3y = saw(t) +
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