Week 9 notes of Physics 3LB lab at University of California, Irvine. Notes are based on the course's lab manual and are intended to help you understand the theory of "Pendula, Natural Frequencies, and Beats."
Wk9: Pendula, Natural Frequencies, and Beats
Sunday, March 1, 2020 9:50 AM
Abbreviation Key:
freq = frequency
Week 9 Lab: Theory Concepts ampl = amplitude
Fig. = figure (of a picture in the lab manual)
w/ = with
• Simple Harmonic Motion: oscillatory behavior is the combination of many sine waves, each b/w = between
w/ their own ampl and freq.
• Natural Frequencies: frequencies at which systems execute simple harmonic motion.
○ Systems only have a few of these.
○ All other behavior can be analyzed in terms of a combination of natural frequencies.
• In this lab, we will study two systems. Each have two degrees of freedom (natural
frequencies).
○ System 1: a pair of speakers, driven at a single freq (lab manual figure says they're at
slightly different freq?).
• Fig.1: function generators powering each speaker. Voltages applied to speakers
will be measured via oscilloscope. Beats monitored by adding the signals to the
oscilloscope and listening in b/w the speakers.
○ System 2: a pair of pendulums coupled by a straw.
• Fig. 2: brass bobs suspended by strings.
• Symmetric Mode: bobs oscillate in the same direction.
• Asymmetric Mode: bobs oscillate in opposite directions. Straw forces bobs to
pivot (abbreviated as h) as string remains stationary.
• Motion of System = Symmetric + Asymmetric
• If both natural frequencies of the system are excited, then "beats" appear at a freq of w1 -
w2.
○ 𝜔𝑏𝑒𝑎𝑡 = 𝜔1 - 𝜔2 (Natural frequencies of the system respectively.)
• Beats: new periodic motion at a freq lower than the natural freq. Differences b/w the natural
frequencies.
• Simple harmonic wave can be described as: 𝜓1 = 𝐴 cos 𝜔1𝑡.
○ 𝜓1 = instantaneous wave ampl
○ A = max ampl
○ w1 = angular wave frequency
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