A 5500 kg railcar hits a bumper (a spring) at 1.3 m/s, and the spring compresses by 0.06 m. Assume no damping. Find k = N/m help (numbers) Hint: Solve the differential equation leaving k as unknown. The compression of the spring is the maximum displacement. It is easiest if you assume that 0 displacement is where the railcar is just touching the bumper. How far does the spring compress when a 6500 kg railcar hits the spring at the same speed? m help (numbers) If the spring would break if it compresses further than 0.26 m, what is the maximum mass of a railcar that can hit it at 1.3 m/s? kg help (numbers) What is the maximum mass of a railcar that can hit the spring without breaking at 2.6 m/s? kg help (numbers)

A 5500 kg railcar hits a bumper (a spring) at 1.3 m/s, and the spring compresses by 0.06 m. Assume no damping. Find k = N/m help (numbers) Hint: Solve the differential equation leaving k as unknown. The compression of the spring is the maximum displacement. It is easiest if you assume that 0 displacement is where the railcar is just touching the bumper. How far does the spring compress when a 6500 kg railcar hits the spring at the same speed? m help (numbers) If the spring would break if it compresses further than 0.26 m, what is the maximum mass of a railcar that can hit it at 1.3 m/s? kg help (numbers) What is the maximum mass of a railcar that can hit the spring without breaking at 2.6 m/s? kg help (numbers)

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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Concept explainers

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

A 5500 kg railcar hits a bumper (a spring) at 1.3 m/s, and the spring compresses by 0.06 m. Assume no damping.
Find k =
N/m help (numbers)
Hint: Solve the differential equation leaving k as unknown. The compression of the spring is the maximum displacement. It is easiest if you assume that 0
displacement is where the railcar is just touching the bumper.
How far does the spring compress when a 6500 kg railcar hits the spring at the same speed?
m help (numbers)
If the spring would break if it compresses further than 0.26 m, what is the maximum mass of a railcar that can hit it at 1.3 m/s?
kg help (numbers)
What is the maximum mass of a railcar that can hit the spring without breaking at 2.6 m/s?
kg help (numbers)

Suppose a spring with spring constant 1 N/m is horizontal and has one end attached to a wall and the other end attached to a mass. You want to use the
spring to weigh items. You put the spring into motion and find the frequency to be 0.9 Hz (cycles per second). What is the mass? Assume there is no friction.
Mass =
help (units)

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