Motion of a mass on a spring suspended vertically

[brayrbob]

Okay I have part of this problem right but am not sure how to proceed on the last part.

A 50 g spring is made from a new steel/titanium alloy. Engineers determine that if a 500 g mass is hung from the spring it oscillates with a period of exactly 1.00 seconds. What is the spring's constant?
Equation used is = system mass = hanging mass + (1/3) spring mass
system mass = 500 + (1/3)50 = 516.6666667
Now I have to use the equation Period^2 = 4pi^2 system mass/spring constant.
I have to solve for mass and don't know how to turn this last equation around.

 

[Doc Al]

You start with this:
$$T^2 = \frac{4 \pi^2 m}{k}$$

To solve for the spring constant, try this: First multiply both sides by $k$, then divide both sides by $T^2$. That will isolate k.

 

[brayrbob]

So then that equation should be k = 4pi^2/T^2?

4pi^2(516.6666667)/1.00^2 = 20397.8243 is the spring constant?