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 12, Problem 12.8P
To determine
The characteristic frequencies and normal modes of the given system.
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Find the nth Taylor polynomial for the function, centered at c.
f(x) = ln(x), n = 4, c = 2
P4(x) =
A simple harmonic oscillator consists of a 100-g mass attached to a spring whose force constant is 10 dyne/cm. The mass is displaced 3 cm and released from rest.The oscillator of Problem 3-1 is set into motion by giving it an initial velocity of 1 cm/s at its equilibrium position. Calculate (a) the maximum displacement and (b) the maximum potential energy.
Prob.1
(i)
State the required conditions of simple harmonic motion (SHH).
(ii)
Consider the torsional pendulum with a moment of inertia I and torsion
constant K. If the pendulum starts its oscillation with an initial angle O, and angular
at t = 0. Obtain the equation of motion and angular frequency of
dt
de
velocity j
%3D
oscillation w. for this pendulum and discuss that it can be classified as SHH.
Show that the torsional angle and angular velocity a of the pendulum for all
time can be expressed as
(iii)
sin wt
0 (t) = 0; coS wt +
w(t) = -w0; sin wt + w cos wt .
Chapter 12 Solutions
Classical Dynamics of Particles and Systems
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