System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.15P
The distance a spring stretches from its “free length” is a function of how much tension is applied to it. The following table gives the spring length y that was produced in a particular spring by the given applied force f. The spring’s free length is 4.7 in. Find a functional relation between f and x, the extension from the free length (y = y − 4.7).
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The elastic potential energy of a spring Ve depends on the spring constant k of the spring and the extension of the spring according to:
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When a beam section is subjected to a shear load, a
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distance y above or below the neutral axis. The average
VQ
shear stress is given by T =
Here V is the shear
It
force on the section, I is the moment of inertia of the
entire section about the neutral axis, and t is the width of
the section at the distance y where the shear stress is
being calculated. Q is the product of the area of the
section above (or below) y and the distance from the
neutral axis to the centroid of that area (Figure 1). In
short, Q is the moment of the area about the neutral axis.
I
Figure
1 of 1
An I-beam has a flange width b = 250 mm, height h = 250 mm, web thickness tw = 9 mm, and flange thickness tf = 14 mm. Use the…
Chapter 1 Solutions
System Dynamics
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Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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