• 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tvt 80x +1000r 2500 cos where x = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of timet (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (b) Determine the value of v for which the solution is undefined (you should present your final answer in miles per hour, as opposed to feet per second).
• 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tvt 80x +1000r 2500 cos where x = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of timet (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (b) Determine the value of v for which the solution is undefined (you should present your final answer in miles per hour, as opposed to feet per second).
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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Question
Transcribed Image Text:• 4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy
road at a constant velocity v. The equation modeling the motion of the car is
Tut
80x + 1000.x = 2500 cos
6.
where x = x (t) represents the vertical position of the cars axle relative to its equilib-
rium position, and the basic units of measurement are feet and feet per second (this
is actually just an example of a forced, un-damped harmonic oscillator, if that is any
help). The constant numbers above are related to the characteristics of the car and
the strut. Note that the coefficient of time t (inside the cosine) in the forcing term
on the right hand side is a frequency, which in this case is directly proportional to the
velocity v of the car.
(b) Determine the value of v for which the solution is undefined (you should present
your final answer in miles per hour, as opposed to feet per second).
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