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H6. Pianos have two or three strings for each note. A piano tuning system called beats occurs as a forced undamped oscillator model when the frequency of excitation is almost equal to the natural frequency of vibration. Suppose the natural frequency of the oscillator is exactly 1/? and that the frequency of the driving function is (1 + ?)/? where ? is a small number, either positive or negative.   a) Write a differential equation with the assumed characteristics.   b) Find the general solution of the differential equation written in item a) when ? = −0.1

H6. Pianos have two or three strings for each note. A piano tuning system called beats occurs as a forced undamped oscillator model when the frequency of excitation is almost equal to the natural frequency of vibration. Suppose the natural frequency of the oscillator is exactly 1/? and that the frequency of the driving function is (1 + ?)/? where ? is a small number, either positive or negative.   a) Write a differential equation with the assumed characteristics.   b) Find the general solution of the differential equation written in item a) when ? = −0.1

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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H6.

Pianos have two or three strings for each note. A piano tuning system called

beats occurs as a forced undamped oscillator model when the frequency of

excitation is almost equal to the natural frequency of vibration. Suppose the natural frequency

of the oscillator is exactly 1/? and that the frequency of the driving function is (1 + ?)/?

where ? is a small number, either positive or negative.

 

a) Write a differential equation with the assumed characteristics.

 

b) Find the general solution of the differential equation written in item a) when ? = −0.1

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