only 5.4 problem, please 80Chapter 5 / The Harmonic5-3. The general solution for the classical harmonic oscillator is x (t) = C sin(wt + p). Showorthat the displacement oscillates between +C and -C with a frequency w radian-s-1v = w/2π cycle-s¯¹. What is the period of the oscillations; that is, how long does it taketo undergo one cycle?5-4. From Problem 5-3, we see that the period of a harmonic vibration is t = 1/v. The averageof the kinetic energy over one cycle is given by(K) =1Interpret the result (K) = (V).-mw²C²2cos² (wt + p)dtShow that (K) = E/2 where E is the total energy. Show also that (V) = E/2, where theinstantaneous potential energy is given bykC²V = sin² (wt + p)2

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)

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter20: Molecular Spectroscopy And Photochemistry

Section: Chapter Questions

Problem 51AP

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