Question

In February 2004, scientists at Purdue University used a highly sensitive technique to measure the mass of a vaccinia virus (the kind used in smallpox vaccine). The procedure involved measuring the frequency of oscillation of a tiny sliver of silicon (just 30.0nm long) with a laser, first without the virus and then after the virus had attached itself to the silicon. The difference in mass caused a change in the frequency. We can model such a process as a mass on a spring.

Part A

Find the ratio of the frequency with the virus attached ( fS+V) to the frequency without the virus (fS) in terms of mV and mS, where mV is the mass of the virus and mS is the mass of the silicon sliver. Notice that it is not necessary to know or measure the force constant of the spring.

Part B

In some data, the silicon sliver has a mass of 2.10

Answer 1

A period of simple harmonic motion done by mass-spring system, is given by T = 2? ?(m/k) and its frequency f = 1/T by f = 1/2? ?(k/m).
The force constant of the spring is the same in both cases, so we write two equations:
f(s+v) = 1/2? ?(k / (ms + mv) ) and f(s) = 1/2? ?(k / ms). The ratio of both frequencies is f(s+v) / f(s) = 1/2? ?(k / (ms + mv) ) / 1/2? ?(k / ms). The force constant k and the 2? factors are cancelled out, and we obtain: f(s+v) / f(s) = ? (ms / (ms + mv)).

To get the mass of the virus, we must solve the above equation for mv. To do so, we must first square both sides of the equation to eliminate the square root: [ f(s+v) / f(s) ]