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 28.0 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 is the formula: f(s+v) / f(s) = √ (ms / (ms + mv))

part B. In some data, the silicon sliver has a mass of 2.10×1^0−16g and a frequency of 2.01×10^15 Hz without the virus and 2.88×10^14 Hz with the virus. What is the mass of the virus in grams?

this is my correct work problem i did below
2.10*10^-16 -[(2.88*10^14/2.01*10^15)^2*2.10*10^-16]/ (2.88*10^14/ 2.01*10^15)^2 and i got 2.1*10^14g which i got wrong ive been stuck with this problem for a while i need help

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1. m(v) = m(s)• [(f(s)/f(sv))^2 -1] =
=2.1•10^-16• [(2.01•10^15/2.88•10^14)^2 -1]=1•10^-14 g

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2. thats wrong

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3. I found the same problem with same answer
A period of simple harmonic motion done by mass-spring system, is given by T = 2π √(m/k) and its frequency f = 1/T by f = 1/2π √(k/m).
The force constant of the spring is the same in both cases, so we write two equations:
f(s+v) = 1/2π √(k / (ms + mv) ) and f(s) = 1/2π √(k / ms). The ratio of both frequencies is f(s+v) / f(s) = 1/2π √(k / (ms + mv) ) / 1/2π √(k / ms). The force constant k and the 2π 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) ]² = ms / (ms + mv). We now multiply both sides by (ms + mv): [ f(s+v) / f(s) ]² (ms + mv) = ms ==> [ f(s+v) / f(s) ]² mv = ms – [ f(s+v) / f(s) ]² ms ==> mv = ms – [ f(s+v) / f(s) ]² ms / [ f(s+v) / f(s) ]² = 2.13×10^-16 g – (2.85×10^14 Hz / 2.04×10^15 Hz)² x 2.13×10^-16 g / (2.85×10^14 Hz / 2.04×10^15 Hz)² = 1.07 x 10^–14 g = 10.7 fg

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4. i did the same way how you should me but i keep getting a wrong answer :/

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