A small fly of mass 0.23 g is caught in a spiders web. The web oscillates predom

Question

A small fly of mass 0.23 g is caught in a spiders web. The web oscillates predominantly with a frequency of 4.7 Hz. What is the value of the effective spring stiffness constant k for the web? Part B: at what frequency would you expect the web to oscillate if an insect of mass 0.46 g were trapped? A small fly of mass 0.23 g is caught in a spiders web. The web oscillates predominantly with a frequency of 4.7 Hz. What is the value of the effective spring stiffness constant k for the web? Part B: at what frequency would you expect the web to oscillate if an insect of mass 0.46 g were trapped? Part B: at what frequency would you expect the web to oscillate if an insect of mass 0.46 g were trapped?

Explanation / Answer

time period of harmonic oscillator is given by

T = 2pi sqrt(m/k)

1/4.7 = 2pi sqrt((0.23/1000)/K )

K= 0.04267616943 N/m

by doubling the mass

T = sqrt(2) * (1/4.7)

so frequency = 1/sqrt(2) * 4.7

3.32340187158 Hz

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