Scientists have developed a clever way to measure a mass of virus using a spring. A cantilever beam in the scanning elec

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Scientists have developed a clever way to measure a mass of
virus using a spring. A cantilever beam in the scanning electron
microscope image below is like a diving board, except that it is
extremely small (a couple of micrometer). The cantilever beam with
mass m can oscillate (imagine a vibrating diving board) and it can
be modeled as a spring with a spring constant k. What you can
measure experimentally is the frequency of oscillation of the
cantilever first without the virus (f1) and after the virus had
attached itself to the cantilever (f2).
(a) Find the mass of virus from f1 and f2 (assume that we don’t
know the spring constant k)
(b) Suppose the mass of cantilever is 10.0 * 10^(-16) g and a
frequency of 2.00 * 10^(15) Hz without the virus and 2.87 * 10^(14)
Hz with the virus. What is the mass of the virus?