Question

 A small fly of mass 0.22 g is caught in a spider’s web. The web oscillates predominantly with a frequency of 4.0 Hz. (a) What is the value of the effective spring stiffness constant k for the web? (b) At what frequency would you expect the web to oscillate if an insect of mass 0.44 g were trapped?

Answer 1

(a) We can find the value of the effective spring stiffness constant $k$ for the web as follows:

$$f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}},$$ $$k=4\pi^2f^2m,$$ $$k=4\pi^2\cdot(4.0\ Hz)^2\cdot0.22\cdot10^{-3}\ kg=0.14\ \dfrac{N}{m}.$$

(b) We can find the frequency of oscillations of the web as follows:

$$f=\dfrac{1}{2\pi}\sqrt{\dfrac{0.14\ \dfrac{N}{m}}{0.44\cdot10^{-3}\ kg}}=2.84\ Hz.$$