How Do You Calculate Spring Constant and Mass for Oscillations?

[dynamity]

Homework Statement

A 200 g mass elongates a spring 3 cm from its equilibrium position. Find the spring constant (k) of the spring in N/m.

An unknown mass is attached to the same spring and set in motion. If the period of oscillation is 3 seconds, find the value of the unknown mass in kg.

Homework Equations

k=mg/x
T=2pi(sqrt)(m/k)

The Attempt at a Solution

I think I've determined part A to be 65.4 N/m. I did this by converting cm->m and g->kg. Then I filled it into the equation...

k=.2(9.81)/.03 = 65.4 N/m

Then I plug it into the other equation for part two of the question

3=2pi(sqrt)m/65.4
3/2pi (changed to .477 for ease)=sqrt(m/65.4)
.477^2=(m/65.4)
.22797=m/65.4
.22797(65.4)=m
m=14.91 kg

Mostly what I'm asking for here is a confirmation on my work and if the m at the end of my second equation comes directly in kg or if it needs to be converted first.

 

[rl.bhat]

Hi dynamity, welcome to PF.
Your answer is correct. Final answer is in kg. No need to convert to any thing.

 

[kerimek]

Your calculations and approach are correct. The value of m at the end of the second equation should be in kg, so there is no need for conversion. Great job on using the correct equations and units! Keep up the good work.