Question

A 2·g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on its feet with a pencil. You discover that you can give the spider the largest amplitude on the thread by tapping exactly once every second. (a) What is the spring constant of the silk thread? N/m (b) After further experimentation, you discover that if you tap at a rate of three times every two seconds, the amplitude is 20% of its maximum value. What is the damping constant for the thread? kg/s

Answer 1

spring constant , k = m ² ...................(1)

one tap is give every one second means frequency f = 1 Hz

Hence spring constant, k = m 4² f² = 210^-3 4² 1 = 0.079 Nm^-1

Amplitude A of damped harmonic motion is given by,

A = A_o e^-b/2m ...........................(2)

where b is damping coefficient and A_o is amplitude of undamped harmonic motion

if A/A_o is 0.2, then from eqn.(2), we have, e^-b/2m = 0.2

Hence, -b/2m = ln(.2) = -1.609     or b = 1.609 2 2 10^-3 = 6.44 10^-3 N s m^-1