Calculate frequency based on change in hanging mass

[EroAlchemist]

Homework Statement

An elastic cord vibrates with a frequency of 3.0 Hz with a mass of 0.60kg is hung from it. What is its frequency when only 0.38kg hangs from it?

Homework Equations

freq = (1/2Pi)*sqrt(k/m)

The Attempt at a Solution

freq = 3.0Hz = (1/2Pi)*sqrt(k/0.60kg)
= (4Pi^2)(9Hz)(.60kg) = k = 853.7 Nm

use k to calc freq:
freq = (1/2Pi)*sqrt(853.7Nm/0.38kg)
Freq = 7.54 Hz

Book gives correct answer as being 3.8 Hz. This seemed simple enough, but I'm obviously missing something. Thanks much for any help.

 

[tiny-tim]

Hi EroAlchemist!

(have a square-root: √ and a pi: π )

the only thing that matters is that it's proportional to 1/√m

nothing else matters, there's no need to do all those calculations to find k and then to eliminate it again …

it just takes time and risks making a mistake!

start again ​

 

[EroAlchemist]

Thanks tiny-tim!
I used f = (1/2π)(√1/.22kg) = 3.35 Hz
That's a closer answer to the book's 3.8Hz answer. However, by not figuring k using the information that the .60kg weight made the spring oscillate at a frequency of 3Hz, I'm not sure how to use the information about the .60kg weight and the 3Hz frequency.

Thanks for the √ and the π
:)
EA

 

[tiny-tim]

it's proportional to 1/√m …

start with 3 Hz, then adjust for the different m