Modeling the motion of the fly on the web as a mass on a spring, at what frequency will the web vibrate when the fly hits it?

A. \(0.91 \mathrm{~Hz}\)

B. \(2.9 \mathrm{~Hz}\)

C. \(9.1 \mathrm{~Hz}\)

D. \(29 \mathrm{~Hz}\)

In fact, spiders carefully adjust the tension of strands to "tune" their web. Suppose an insect lands and is trapped in a web. The silk of the web serves as the spring in a spring-mass system while the body of the insect is the mass. The frequency of oscillation depends on the restoring force of the web and the mass of the insect. Spiders respond more quickly to larger-and therefore more valuable-prey, which they can distinguish by the web's oscillation frequency.

Suppose a \(12 \mathrm{mg}\) fly lands in the center of a horizontal spider's web, causing the web to sag by \(3.0 \mathrm{~mm}\).