Elastic Restoring Force- Spring Constant

[~Callaway~]

Homework Statement

A bug having a mass of 0.20g falls into a spider's web, setting it into vibration with a dominant frequency of 18 Hz. Find the corresponding spring constant.

Homework Equations

1. f=[tex]\frac{1}{T}[/tex]

2. [tex]\omega[/tex]=2[tex]\pi[/tex]f

3. [natural angular frequency], [tex]\omega[/tex]₀=[tex]\sqrt{\frac{k}{m}}[/tex]

4. [natural linear frequency], f₀=[tex]\frac{1}{2\pi}[/tex]*[tex]\sqrt{\frac{k}{m}}[/tex]

The Attempt at a Solution

My thought was to plug the mass in for m and the frequency in for f₀ and then solve for k in equation 4, but I am getting an answer very different from the given answer, which is 2.6 N/m. My main question is on the units of the spring constant, I think I am missing just where this unit arises from, and I think I should be able to solve the problem if I can understand that, but I must be missing something. I would very much appreciate any thoughts on this.

 

[~Callaway~]

Addendum: continued working and solved problem, but here is answer in case anybody else on this forum has a similar problem/issue.

To calculate spring constant from frequency and mass:

Start with equation T=2[tex]\pi[/tex][tex]\sqrt{\frac{m}{k}}[/tex]

Use algebra to solve for k, k=4[tex]\pi²[/tex]*m*T²

Know that T is frequency, so plug in Hz for T and be sure to convert mass to kilograms..

Giving final answer of 2.5582~2.6N/m