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

The unknown mass is 3.87 kg.

Step-by-step 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{(m)/(k) }`

where;

m is the mass attached to the spring

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

Therefore, the unknown mass is 3.87 kg.