7. We reconsider the spring system of Homework Set 3, #5. As before, the spring has stiffness k = 30 N/m, is damped with damping constant b= 18 kg/s, and is attached to a weight with mass M =3 kg. However, now we impose the following discontinuous oscillation of the support (in Newtons; see figure at left): %3D -117 sin t, F() ={0, 0sts 27, t> 27. %3D Initially the spring is extended 1 m and let go. (a) Solve the resulting system for the displacement r(t) in the region t e (0, 27]. (b) Show that x(27) = -e-6r + 2, i(27) = 3(e-6 - 1). (4.3) (c) Using the fact that z and should be continuous at t = 27, calculate the displacement a in the region t > 27.
7. We reconsider the spring system of Homework Set 3, #5. As before, the spring has stiffness k = 30 N/m, is damped with damping constant b= 18 kg/s, and is attached to a weight with mass M =3 kg. However, now we impose the following discontinuous oscillation of the support (in Newtons; see figure at left): %3D -117 sin t, F() ={0, 0sts 27, t> 27. %3D Initially the spring is extended 1 m and let go. (a) Solve the resulting system for the displacement r(t) in the region t e (0, 27]. (b) Show that x(27) = -e-6r + 2, i(27) = 3(e-6 - 1). (4.3) (c) Using the fact that z and should be continuous at t = 27, calculate the displacement a in the region t > 27.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
7
Transcribed Image Text:30 N/m
3 kg
ss
(-117 sin t) N
18 kg/s
![7. We reconsider the spring system of Homework Set 3, #5. As before, the spring
has stiffness k = 30 N/m, is damped with damping constant b= 18 kg/s, and is
attached to a weight with mass M = 3 kg. However, now we impose the following
discontinuous oscillation of the support (in Newtons; see figure at left):
%3D
%3D
%3D
(-117 sin t,
F(t) ={0.
0St< 27,
t > 27.
Initially the spring is extended 1 m and let go.
(a) Solve the resulting system for the displacement r(t) in the region t e [0, 2].
(b) Show that
x(2m) = -e-6 + 2,
i(27) = 3(e-6 – 1).
(4.3)
%3D
%3D
(c) Using the fact that a and i should be continuous at t = 27, calculate the
displacement a in the region t > 27.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40fcc70f-775e-4741-8507-dd44e1e11495%2F44b63cdf-6887-429d-b3da-350f4f03fda4%2Fgwczp7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. We reconsider the spring system of Homework Set 3, #5. As before, the spring
has stiffness k = 30 N/m, is damped with damping constant b= 18 kg/s, and is
attached to a weight with mass M = 3 kg. However, now we impose the following
discontinuous oscillation of the support (in Newtons; see figure at left):
%3D
%3D
%3D
(-117 sin t,
F(t) ={0.
0St< 27,
t > 27.
Initially the spring is extended 1 m and let go.
(a) Solve the resulting system for the displacement r(t) in the region t e [0, 2].
(b) Show that
x(2m) = -e-6 + 2,
i(27) = 3(e-6 – 1).
(4.3)
%3D
%3D
(c) Using the fact that a and i should be continuous at t = 27, calculate the
displacement a in the region t > 27.
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