Suppose the lateral displacement of the center of a bridge may be modeled as a spring-and-mass system, with low friction and a high spring constant. Let z = r(t) be the lateral displacement of the center of the bridge, let m>0 be the mass, and let k> 0 be the spring constant. Neglect the effect of friction, and consider an external wind force w(t) acting on the center of the bridge. Then r(t) obeys the differential equation + kr = w(t) m dt2 Find a wind force function w = w(t) with ||w||x = max Jw(t)| < 1 that will definitely result in the bridge collapsing in time, and explain why the bridge will eventually collapse with this choice of w. tER

Suppose the lateral displacement of the center of a bridge may be modeled as a spring-and-mass system, with low friction and a high spring constant. Let z = r(t) be the lateral displacement of the center of the bridge, let m>0 be the mass, and let k> 0 be the spring constant. Neglect the effect of friction, and consider an external wind force w(t) acting on the center of the bridge. Then r(t) obeys the differential equation + kr = w(t) m dt2 Find a wind force function w = w(t) with ||w||x = max Jw(t)| < 1 that will definitely result in the bridge collapsing in time, and explain why the bridge will eventually collapse with this choice of w. tER

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Solution to HW problem.

Suppose the lateral displacement of the center of a bridge may be modeled as
a spring-and-mass system, with low friction and a high spring constant. Let r = 1(t) be
the lateral displacement of the center of the bridge, let m>0 be the mass, and let k > 0
be the spring constant. Neglect the effect of friction, and consider an external wind force
w(t) acting on the center of the bridge. Then r(t) obeys the differential equation
+ kr = w(t)
m
dt?
Find a wind force function w = w(t) with ||w|| = max |w(t)| <1 that will definitely
tER
result in the bridge collapsing in time, and explain why the bridge will eventually collapse
with this choice of w.

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