Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Question
Chapter 3, Problem 3.38P
To determine
The response of a damped oscillator to a forcing function of the form
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A spring/mass/dashpot system has mass 5 kg, damping constant 70 kg/sec and spring constant 845
kg/sec/sec. Express the ODE for the system in the form
a"+ 2px' + wr = 0
Identify the natural (undamped) frequency of the spring:
wo 3=
(square Hz)
Identify the parameter p:
(Hz)
Now assume that the system has the oscillating forcing function cos(wod) with the same frequendy as the
spring's natural frequency.
+ 14a'+ 169a =
cos(wat)
Find the general solution.
Consider a particle subject to a linear restoring force F=-kx, where k is a constant and x
is the position of the particle relative to equilibrium (x-0). Classically, if the particle is
displaced from its equilibrium position and released, it oscillates between the points x=-A
and x=+A, where A is the amplitude of the motion. Derive an expression for the total
energy of the oscillator. Take x=Asinwt
A spring/mass/dashpot system has mass 16 kg, damping constant 448 kg/sec and spring constant 5776
kg/sec/sec. Express the ODE for the system in the form
x"+2px'+w²x = 0
Identify the natural (undamped) frequency of the spring:
wo =
Identify the parameter p:
p =
Xp
(square Hz)
Now assume that the system has the oscillating forcing function cos(wot) with the same frequency as the
spring's natural frequency. Complexify the ODE and use the real part as a particular solution:
x"+28x'+361x = cos(wot)
=
(Hz)
(meters)
Chapter 3 Solutions
Classical Dynamics of Particles and Systems
Ch. 3 - Prob. 3.1PCh. 3 - Allow the motion in the preceding problem to take...Ch. 3 - Prob. 3.3PCh. 3 - Prob. 3.4PCh. 3 - Obtain an expression for the fraction of a...Ch. 3 - Two masses m1 = 100 g and m2 = 200 g slide freely...Ch. 3 - Prob. 3.7PCh. 3 - Prob. 3.8PCh. 3 - A particle of mass m is at rest at the end of a...Ch. 3 - If the amplitude of a damped oscillator decreases...
Ch. 3 - Prob. 3.11PCh. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Reproduce Figures 3-10b and c for the same values...Ch. 3 - Prob. 3.16PCh. 3 - For a damped, driven oscillator, show that the...Ch. 3 - Show that, if a driven oscillator is only lightly...Ch. 3 - Prob. 3.19PCh. 3 - Plot a velocity resonance curve for a driven,...Ch. 3 - Let the initial position and speed of an...Ch. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Obtain the response of a linear oscillator to a...Ch. 3 - Calculate the maximum values of the amplitudes of...Ch. 3 - Consider an undamped linear oscillator with a...Ch. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - An automobile with a mass of 1000 kg, including...Ch. 3 - Prob. 3.41PCh. 3 - An undamped driven harmonic oscillator satisfies...Ch. 3 - Consider a damped harmonic oscillator. After four...Ch. 3 - A grandfather clock has a pendulum length of 0.7 m...
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