5. (a) Using Laplace Transforms and the Bromwich integral method for the inverse, solve the differential equation y" + 2y' + y = f(t), with y(0) = y(0) = 0, where f(t) = S(t-1) + 8(t− 2). (b) Physical interpretation: the above equations correspond to the dis- placements of a block of mass m = 1 kg attached to a spring sitting on a table. There is friction between the table and the block propor- tional to the velocity of the block: which term is this? Is the sign in agreement with your intuition? Explain. What is the value of the spring constant k in Newton/meter (the force from the spring goes as F = -ky)? = The two deltas on the right-hand side correspond to hammering in- cidents, where the block was suddenly hit at t 1 and t = 2 s. (c) Produce a plot of the spring displacement versus time. Interpret the results. In particular: is the spring oscillating after the hammering incidents? Explain.
5. (a) Using Laplace Transforms and the Bromwich integral method for the inverse, solve the differential equation y" + 2y' + y = f(t), with y(0) = y(0) = 0, where f(t) = S(t-1) + 8(t− 2). (b) Physical interpretation: the above equations correspond to the dis- placements of a block of mass m = 1 kg attached to a spring sitting on a table. There is friction between the table and the block propor- tional to the velocity of the block: which term is this? Is the sign in agreement with your intuition? Explain. What is the value of the spring constant k in Newton/meter (the force from the spring goes as F = -ky)? = The two deltas on the right-hand side correspond to hammering in- cidents, where the block was suddenly hit at t 1 and t = 2 s. (c) Produce a plot of the spring displacement versus time. Interpret the results. In particular: is the spring oscillating after the hammering incidents? Explain.
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:5. (a) Using Laplace Transforms and the Bromwich integral method for
the inverse, solve the differential equation y” + 2y' + y = f(t), with
y(0) = ý(0) = 0, where
ƒ (t) = S(t − 1) + 8(t − 2).
(b) Physical interpretation: the above equations correspond to the dis-
placements of a block of mass m = 1 kg attached to a spring sitting
on a table. There is friction between the table and the block propor-
tional to the velocity of the block: which term is this? Is the sign
in agreement with your intuition? Explain. What is the value of the
spring constant k in Newton/meter (the force from the spring goes
as F = -ky)?
The two deltas on the right-hand side correspond to hammering in-
cidents, where the block was suddenly hit at t = 1 and t = 2 s.
(c) Produce a plot of the spring displacement versus time. Interpret the
results. In particular: is the spring oscillating after the hammering
incidents? Explain.
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