Question

A 1.9 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 his feet with a pencil. you soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap at a frequency of 1.2 hz. what is the spring constant of the silk thread?

Answer 1

m = 1.9 g = 1.9 x 10⁻³ kg, the mass of the spider
f = 1.2 Hz, the fundamental frequency

The circular frequency is
ω = 2πf = 2.4π cycles/s

For oscillatory motion,
ω² = k/m
where k =  the spring constant.
Therefore
k/m = (2.4π)²
k = (1.9 x 10⁻³ kg)*(2.4π 1/s)² = 0.108 N/m

Answer: 0.108 N/m