A rail road bumper is designed as a spring in parallel with a viscous damper. Whatis the bumper's damping coefficient such that the system has a damping ratio of1.25, when the bumper is engaged by a rail car of 20,000 kg mass. The stiffnessof the spring is 200 kN/m. If the rail car engages the bumper, while traveling at aspeed of 20m/s, what is the maximum deflection of the bumper?poooom

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Mechanical Engineering

what is the maximum deflection of the bumper?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

A rail road bumper is designed as a spring in parallel with a viscous damper. What
is the bumper's damping coefficient such that the system has a damping ratio of
1.25, when the bumper is engaged by a rail car of 20,000 kg mass. The stiffness
of the spring is 200 kN/m. If the rail car engages the bumper, while traveling at a
speed of 20m/s, what is the maximum deflection of the bumper?
poooo
m

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Step 1: Calculate the natural frequency.

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Step 2: Write the general equation for free damped vibration and substitute the given values.

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Step 3: Find the roots of complementary function.

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Step 4: Write the general equation for real roots.

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Step 5: Find constant values A and B, substitute in general equation.

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Step 6: Find the maximum deflection using derived equation.(minimum value of time, t=0)

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