Question

An unknown mass is hung from a very light spring with a spring constant of 13.6 N/m. Neglect the mass of the spring. If the period of oscillation of the mass-spring system is 3.35 s, then the unknown mass is:__________

Answer 1

Answer:

The unknown mass is 3.87 kg.

Explanation:

Given;

spring constant of the spring, k = 13.6 N/m

period of oscillation, T = 3.35 s

The period of oscillation of the mass-spring system is given by;

$T = 2\pi \sqrt{\frac{m}{k} }$

where;

m is the mass attached to the spring

$T = 2\pi \sqrt{\frac{m}{k} }\\\\\frac{T}{2\pi} = \sqrt{\frac{m}{k} }\\\\\frac{T^2}{4\pi^2}= \frac{m}{k}\\\\m = \frac{kT^2}{4\pi^2}\\\\m = \frac{(13.6)(3.35)^2}{4\pi^2}\\\\m = 3.87 \ kg$

Therefore, the unknown mass is 3.87 kg.