System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.31P
Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 9.5 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height Constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table.
Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest.
A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball.
The bullet embeds itself inside the ball.
How high (h) do the ball and the bullet rise?
Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt.
Need handwritten solution.
Mechanical engineering
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
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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