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Intro to Harmonic Oscillator

Intro to Harmonic Oscillator. Ankit , Donghun and Masha 4/2/2014. Intended for an intro physics course for non-physics majors (premeds). Learning Objectives. You will learn about the natural frequency of a mass-spring harmonic oscillator system.

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Intro to Harmonic Oscillator

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  1. Intro to Harmonic Oscillator Ankit, Donghun and Masha 4/2/2014 Intended for an intro physics course for non-physics majors (premeds)

  2. Learning Objectives • You will learn about the natural frequency of a mass-spring harmonic oscillator system. • You will be able to predict how changing the mass of a harmonic oscillator affects the frequency. • You will be able to use the mass, spring constant, frequency relationship to interpret features of molecular vibration spectrum. • You will recognize the relationship between natural frequency and resonance.

  3. Q: Consider two oscillators (Q and R) composed of identical springs with masses m and 4m attached to them. How will the natural frequencies of the oscillators compare? A. fQ= fR B. fQ< fR C. fQ> fR D. Can’t tell E. None of the above Q R m 4m

  4. Q: Consider two oscillators (Q and R) composed of identical springs with masses m and 4m attached to them. How will the natural frequencies of the oscillators compare? A. fQ= fR B. fQ = 4fR C. fQ= ¼fR D. fQ = 2fR E. fQ = ½fR Q R m 4m

  5. How will the natural frequencies of the oscillators compare? Answer: D. fQ = 2fR Q R m 4m (N/m) (Hz) (kg)

  6. Discussion question • What do you think will happen if you jiggle the mass at a frequency close to the natural frequency? • Give it a try! Discuss what you think is happening with your group.

  7. Resonance examples Music • All musical instruments produce sound via a vibrating element • In a violin, the differing thicknesses of the strings result in different resonant frequencies • The musician touches the instrument to change the resonance, ie pitch, of the sound played • Architecture • Bridges, tall buildings and other structures are susceptible to collapse when driven at their natural frequency by external factors like wind or people walking Tacoma Narrows Bridge • Everyday phenomena • Swings • Wine glass vibration http://education-portal.com/academy/lesson/resonance-definition-transmission-of-waves.html#lesson http://www.kshitij-school.com/Study-Material/Class-11/Physics/Superposition-and-standing-waves/Resonance-standing-waves.aspx

  8. Diatomic molecule Note: take much heavier Cl atom to be stationary (like a wall) m (H or D) Cl

  9. Vibrational energy levels HCl DCl n=7 n=6 n=5 n=7 n=6 n=4 n=5 Energy n=3 n=4 n=3 n=2 n=2 n=1 n=1 n=0 n=0

  10. Vibrational Spectrum of HCl and DCl HCl f = 8.555 x 1013 Hz DCl f = 6.216 x 1013 Hz cf. f= 6.049 x 1013 Hz Absorption (a.u.) Frequency (Hz) D. E. Mann et al., J. Chem. Phys. 44 3453 (1966)

  11. Vibrational Spectrum of HCl and DCl H35Cl f = 8.555 x 1013 Hz D35Cl f = 6.216 x 1013 Hz D37Cl H37Cl Absorption (a.u.) Frequency (Hz) D. E. Mann et al., J. Chem. Phys. 44 3453 (1966) HCl From http://hyperphysics.phy-astr.gsu.edu

  12. Next Class: Damped Harmonic Oscillator f ? f ? f ? Vacuum Air Water

  13. Homework: diatomic molecule with similar masses m1m2 m1m2 m2 m1 m1 m2

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