The spring-mass system in Problem 6 is modified by introduction of an external driving force, F(t). The resulting differential equation for the motion is d'y dt2 2- + 32y(t) = F(t). %3D Problem 9. For an external force, F(t) = 28 cos(3t), find the function y(t) that describes the motion of the mass. Does the motion remain bounded as t → +o0? Explain your answer. Problem 10. For an external force, F(t) = 28 cos(4t), find the function y(t) that describes the motion of the mass. In this case, the frequency of the system and the external force are the same resulting in a phenomenon known as resonance. Describe what happens as ++ +oo?
The spring-mass system in Problem 6 is modified by introduction of an external driving force, F(t). The resulting differential equation for the motion is d'y dt2 2- + 32y(t) = F(t). %3D Problem 9. For an external force, F(t) = 28 cos(3t), find the function y(t) that describes the motion of the mass. Does the motion remain bounded as t → +o0? Explain your answer. Problem 10. For an external force, F(t) = 28 cos(4t), find the function y(t) that describes the motion of the mass. In this case, the frequency of the system and the external force are the same resulting in a phenomenon known as resonance. Describe what happens as ++ +oo?
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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Please solve problem 10
Transcribed Image Text:The spring-mass system in Problem 6 is modified by introduction of an external
driving force, F(t). The resulting differential equation for the motion is
&y
2-
dt2
+ 32y(t) = F(t).
Problem 9. For an external force, F(t) = 28 cos(3t), find the function y(t) that describes
the motion of the mass. Does the motion remain bounded as t→ +o? Explain your answer.
Problem 10. For an external force, F(t) = 28 cos(4t), find the function y(t) that describes
the motion of the mass. In this case, the frequency of the system and the external force
are the same resulting in a phenomenon known as resonance.
t + +oo?
Describe what happens as
Transcribed Image Text:Problems 6 though 10 involve modelling the motion of an object attached to
a spring. The function, y(t), denotes the displacement of the mass from the
equilibrium position, and is a function of time, t. The velocity and acceleration
are
dy
v(t) = y'(t) =
dt
dy
a(t) = y"(t) =
dt2
and
respectively.
All work, solutions and answers should be written in terms of t.
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