Question

How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 n/m so that it will oscillate at 1.00 hz?

Answer 1

The frequency of a simple harmonic oscillator such as a spring-mass system is given by

`f= (1)/(2 \pi) \sqrt{ (k)/(m) }`
where
k is the spring constant
m is the mass attached to the spring.

Re-arranging the formula, we get:

`m= (k)/(4 \pi^2 f^2)`
and since we know the constant of the spring:

`k=39.5 N/m`
and the frequency of oscillation:
f=1.00 Hz
we can find the value of the mass attached to it:

`m= (39.5 Hz)/(4 \pi^2 (1.00 Hz)^2) = 1.00 kg`