Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 23.1, Problem 3eTH
(i)
To determine
The pulse at 0.3 s.
(ii)
To determine
Inconsistency with the free-end boundary condition for the given pulse.
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A uniform slender rod of length L and mass m is pinned at point "O' and connected to a linear
spring of stiffness k as shown in Figure la.
i. Determine the relationship that defines stability of the undamped system.
ii. A linear dashpot of damping coefficient c is added to the system as shown in Figure 1b.
Given the following parameters:
L=0.4 m, b=0.1 m, m=1.5 kg, k = 50 N/m and c =100 Ns/m,
determine an expression for the response of the system if the initial angular displacement
and initial angular velocity are 0 rad and 1.5 rad/s respectively.
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Figure la
Figure 1b
Consider the waveforms given below
1. Determine the dimensionality of the waveforms and a set of basis functions.
2. Use the basis functions to represent the four waveforms by vectors s1, s2,
S3, S4.
3. Determine the minimum distance between any pair of vectors.
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1. Write the general equation for the spherical harmonic Y; (0, p) and identify Om(), P' (cos 0), and the
normalization constant.
2. Show that Y, (0, $) is an eigenfunction of L². What is the eigenvalue?
3. Show that Y (0,¢) and Y†'(0, p) are orthogonal.
Chapter 23 Solutions
Tutorials in Introductory Physics
Ch. 23.1 - Prob. 1THCh. 23.1 - In the spaces provided belowright, carefully draw...Ch. 23.1 - Prob. 2bTHCh. 23.1 - We begin by considering the forces exerted on a...Ch. 23.1 - Prob. 3bTHCh. 23.1 - Prob. 3cTHCh. 23.1 - Prob. 3dTHCh. 23.1 - Prob. 3eTHCh. 23.1 - Prob. 4THCh. 23.2 - Prob. 1TH
Ch. 23.2 - Prob. 2aTHCh. 23.2 - Prob. 2bTHCh. 23.2 - Prob. 2cTHCh. 23.2 - Prob. 3aTHCh. 23.2 - Prob. 3bTHCh. 23.2 - Prob. 3cTHCh. 23.2 - The figure at right has several errors. How many...Ch. 23.3 - Prob. 1aTHCh. 23.3 - Prob. 1bTHCh. 23.3 - Prob. 1cTHCh. 23.3 - For each of the periodic functions below, indicate...Ch. 23.3 - Prob. 2THCh. 23.3 - Use trigonometry to determine the mathematical...Ch. 23.3 - Starting from the equation that you wrote above,...Ch. 23.3 - Suppose the speed of the refracted wave were half...Ch. 23.3 - Prob. 3dTHCh. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - A long, thin steel wire is cut in half, and each...Ch. 23.4 - Consider an instant when the fields are nonzero at...Ch. 23.4 - How would your answers to parta be different if...Ch. 23.4 - Prob. 3TH
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