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to undergo one cycle? 5-4. From Problem 5-3, we see that the period of a harmonic vibration is t = 1/v. The average of the kinetic energy over one cycle is given by 1 ==S T (K) = Interpret the result (K) = (V). mw²C² 2 Show that (K) = E/2 where E is the total energy. Show also that (V) = E/2, where the instantaneous potential energy is given by V = kC² cos² (wt + p)dt 2 - sin² (wt + p)

to undergo one cycle? 5-4. From Problem 5-3, we see that the period of a harmonic vibration is t = 1/v. The average of the kinetic energy over one cycle is given by 1 ==S T (K) = Interpret the result (K) = (V). mw²C² 2 Show that (K) = E/2 where E is the total energy. Show also that (V) = E/2, where the instantaneous potential energy is given by V = kC² cos² (wt + p)dt 2 - sin² (wt + p)

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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only 5.4 problem, please

80 Chapter 5 / The Harmonic 5-3. The general solution for the classical harmonic oscillator is x (t) = C sin(wt + p). Show or that the displacement oscillates between +C and -C with a frequency w radian-s-1 v = w/2π cycle-s¯¹. What is the period of the oscillations; that is, how long does it take to undergo one cycle? 5-4. From Problem 5-3, we see that the period of a harmonic vibration is t = 1/v. The average of the kinetic energy over one cycle is given by (K) = 1 Interpret the result (K) = (V). - mw²C² 2 cos² (wt + p)dt Show that (K) = E/2 where E is the total energy. Show also that (V) = E/2, where the instantaneous potential energy is given by kC² V = sin² (wt + p) 2
Transcribed Image Text:80 Chapter 5 / The Harmonic 5-3. The general solution for the classical harmonic oscillator is x (t) = C sin(wt + p). Show or that the displacement oscillates between +C and -C with a frequency w radian-s-1 v = w/2π cycle-s¯¹. What is the period of the oscillations; that is, how long does it take to undergo one cycle? 5-4. From Problem 5-3, we see that the period of a harmonic vibration is t = 1/v. The average of the kinetic energy over one cycle is given by (K) = 1 Interpret the result (K) = (V). - mw²C² 2 cos² (wt + p)dt Show that (K) = E/2 where E is the total energy. Show also that (V) = E/2, where the instantaneous potential energy is given by kC² V = sin² (wt + p) 2
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