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hadoque
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Homework Statement
Model the vibrating quartz-crystal thickness monitor as a mass(m)-spring combination, where k is the spring constant.
a) What is the resonant frequency?
b) Show that as additional mass [tex]\delta m[/tex] deposits the the difference in resonant frequency or frequency shift is given by [tex]\Delta f \approx f_0 \delta m /2m[/tex] for [tex]\delta m / m \ll 1[/tex]
Homework Equations
The Attempt at a Solution
a) F=-kx
[tex]f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}[/tex]
b) [tex]\Delta f = \frac{1}{2 \pi} \sqrt{\frac{k}{\delta m +m}} - f_0[/tex]
Is this equation the right approach? Seems difficult to eliminate one whole term on the right side, and the k, how to get rid of that?