# Relating force constant and frequency to mass

1. Sep 11, 2007

### Vidatu

1. The problem statement, all variables and given/known data

A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of 5.65 Hz.

Find the mass of the object.

2. Relevant equations

F=-kx
F=ma
No idea what else...

3. The attempt at a solution

No idea where to start. I get to:

ma=-kx
m = (-123x) / (a)

and can't think where to go from there. I've tried:

1cycle=4 max displacments (x), so
f=5.65Hz = 22.6 cycles of x /s

thereby returning x as .25, but that's dead wrong. Any ideas? I'm totally lost.

Last edited: Sep 11, 2007
2. Sep 11, 2007

### andrevdh

The mass executes simple harmonic motion. In the relevant theory you can find a relation between the period of oscillations, the mass of the object and the force contant.

3. Sep 11, 2007

### Vidatu

Alright, I got it.

T = 2(pi)*sqrt(m/k)

m = k * (T/(2(pi)))^2 = 9.76E-2

Just for curiosity's sake, was there any other way to do it, that wasn't much harder?

4. Sep 12, 2007

### andrevdh

That's the only way I know of.

5. Sep 14, 2007

### dynamicsolo

If you're in a calculus-based course, you might be expected to know *how* to get from the force equation F = ma = -kx to the result for the period. But, in the end, you would still apply the period formula you used here.