A 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with damping constant c = 7 N-sec/m. The object is initially displaced 5 m above equilibrium and released. Find its displacement and time-varying amplitude for t > 0. y(t) : The motion in this example is O critically damped overdamped O underdamped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) = 4 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? What is the maximum possible amplitude?
A 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with damping constant c = 7 N-sec/m. The object is initially displaced 5 m above equilibrium and released. Find its displacement and time-varying amplitude for t > 0. y(t) : The motion in this example is O critically damped overdamped O underdamped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) = 4 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? What is the maximum possible amplitude?
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:Let the initial amplitude be k = 71.5, the damping constant be
Answers should be in exact form (i.e., do not use a calculator to get a decimal approximation).
3, and the frequency be f = 4.5.
||
ct
a. Find a function of the form y
ke
cos (wt) that models the damped harmonic motion.
y =
b. Sketch the graph the function.
Transcribed Image Text:A 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with
damping constant c = 7 N-sec/m. The object is initially displaced 5 m above equilibrium and released.
Find its displacement and time-varying amplitude for t > 0.
y(t)
The motion in this example is
O critically damped
overdamped
O underdamped
Consider the same setup above, but now suppose the object is under the influence of an outside force
given by F(t) = 4 cos(wt).
What value for w will produce the maximum possible amplitude for the steady state component of the
solution?
What is the maximum possible amplitude?
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