Question

A person wants to make a metronome for music practice. He uses a 35-g object attached to a spring to serve as the time standard.

What is the desired spring constant of the spring if the object needs to make 1.00 vibrations each second?

Assume that the spring obeys Hookes law, and ignore any possible damping due to air resistance or friction.

Answer 1

To develop this problem it will be necessary to apply the concepts related to the frequency of a spring mass system, for which it is necessary that its mathematical function is described as

$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

Here,

k = Spring constant

m = Mass

Our values are given as,

$m = 35g = 35*10^{-3}kg$

$f = 1 Hz$

Rearranging to find the spring constant we have that,

$k = (2\pi f \sqrt{m})^2$

$k = 4\pi^2 f^2 m$

$k = (4) (\pi)^2 (1) (35*10^{-3})$

$k = 1.38N/m$

Therefore the spring constant is 1.38N/m