<p>an insect trapped in a spiders web is subject to a restoring force of a hooke

Question

<p>an insect trapped in a spiders web is subject to a restoring force of a hooke's law type. As it struggles the web is distroted and spring forces act to keep the web flat. So it is possible to ascribe an effective spring constant to a web.&#160; In this case a 1 gram bug casues the web to vibrate 15 times a second, that is the web completes 15.2 oscillations per second.</p>
<p>&#160;</p>
<p>what is the peroid for one oscillation, what is the spring constant of the web...and if a 4 graM bug was caught what would be the number of oscillations in one second</p>

Explanation / Answer

a) The time period one oscillation T = 1/15.2 = 0.0657 s

    Spring constant k = 4 2 m / T2

                               = 4 x 3.142 x 10-3 / 0.0657            ( here m = 1 gram = 10-3 kg)

                               = 0.600 N/m

b)   T' = 2 m'/k

         = 2 x 3.14 x 4 x 10-3 / 0.600

         = 0.5127 s

   Therefore

         n = 1 / 0.5127 = 1.95 oscillations per second

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