How Does Cutting a Spring Affect Its Angular Frequency?

[JSmith89]

Homework Statement

A 60-coil spring has a spring constant of 434 N/m. It is cut into two shorter springs, each of which has 30 coils. One end of a 30-coil spring is attached to a wall. An object of mass 45.1 kg is attached to the other end of the spring, and the system is set into horizontal oscillation. What is the angular frequency of the motion?

Homework Equations

[tex]\omega[/tex]=[tex]\sqrt{}k/m[/tex]

if that didn't come out right, w(omega)=the square root of k/m

The Attempt at a Solution

I believe this is the right equation, but I don't know how to factor in the spring that is cut into two separate ones...like how/if it affects the spring constant or another variable. Thanks in advance! :-)

 

[tiny-tim]

spring!

I believe this is the right equation, but I don't know how to factor in the spring that is cut into two separate ones...like how/if it affects the spring constant or another variable.

Hi JSmith89!

Look at it from first principles …

How is the spring constant defined?

Imagine the spring being compressed while still in one piece …

how is each half affected?

And so what is the spring constant of each half?

 

[JSmith89]

ok got it. each half will have a spring constant of 2k. thanks for your help!