Question

oscillating spring mass systems can be used to experimentally determine an unknown mass without using a mass balance. a student observes that a particular spring-mass system has a frequency of oscillation of 10 Hz. the spring constant of the spring is 250 N/m. what is the mass?​

Answer 1

let w = 2 pi f
F = m a = -k x
if x = sin w t
then a = -w^2 x
- mw^2 = -k
w^2 = k/m
(2 pi f)^2 = k/m
so
m = k / (2 pi f)^2 = 250 / (20 pi)^2 = 250 / 3944 = .0634 kg = 63.4 grams