PHYS 20 LESSONS: INTRO Lesson 1: Intro to CH Physics Measurement.
Intro to Harmonic Oscillator Ankit, Donghun and Masha 4/2/2014 Intended for an intro physics course...
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Transcript of Intro to Harmonic Oscillator Ankit, Donghun and Masha 4/2/2014 Intended for an intro physics course...
Intro to Harmonic Oscillator
Ankit, Donghun and Masha4/2/2014
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.
• 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.
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
mQ
4mR
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
mQ
4mR
How will the natural frequencies of the oscillators compare?
Answer: D. fQ = 2fR
mQ
4mR𝒇=𝟏𝟐𝝅 √ 𝒌
𝒎(Hz)
(N/m)
(kg)
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.
Resonance examplesMusic• 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
Everyday phenomena • Swings• Wine glass vibration
http://education-portal.com/academy/lesson/resonance-definition-transmission-of-waves.html#lessonhttp://www.kshitij-school.com/Study-Material/Class-11/Physics/Superposition-and-standing-waves/Resonance-standing-waves.aspx
Tacoma Narrows Bridge
D. E. Mann et al., J. Chem. Phys. 44 3453 (1966)
HCl f = 8.555 x 1013 Hz
Abso
rptio
n (a
.u.)
Frequency (Hz)
DCl f = 6.216 x 1013 Hz
Vibrational Spectrum of HCl and DCl
cf. f = 6.049 x 1013 Hz
From http://hyperphysics.phy-astr.gsu.edu
HCl
D. E. Mann et al., J. Chem. Phys. 44 3453 (1966)
H35Cl f = 8.555 x 1013 Hz
H37Cl
Abso
rptio
n (a
.u.)
Frequency (Hz)
D35Cl f = 6.216 x 1013 Hz
D37Cl
Vibrational Spectrum of HCl and DCl