Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 3, Problem 3.27P
To determine
Show that Equation 3.89 can be expressed as
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Ex. 946. Given x(t)=220.0 on the interval t=[-2.80,0] milliseconds and x(t)=0
elsewhere.
Determine the Fourier transform of x(t), which is X(f) where f
Determine X (f)_real, X(f)_imaginary,
is frequency in Hertz.
X(f)_amplitude,
and X(f) radians, all evaluated at f=80.0 Hertz. ans:4
The Fourier transform of a function f (x) is defined as:
f (w) = L dx
f (ω) -.
f (x)e-iwx
Similarly, the inverse Fourier transform of a function
f (w) whose Fourier transform is known is found as:
1
f(x) = L f (w) e-iwx dw
So, find the Fourier transform f (w) for a> 0 of the
function given below, and using this result, calculate the
inverse Fourier transform to verify the form f (x) given to
you:
for x > 0
for x <0
e-ax,
f (x) = }{
Let D = 3.00r2 ar μC/m2 for r ≤ 0.05 cm and D = (0.25/r2) ar μC/m2 for r ≥ 0.05 m. Find ρν for r = 0.03 m.
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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