Calculating Mass & Spring Constant for Oscillation

[QuantumKnight]

Homework Statement

A block with mass m is attached to the end of a spring with a constant spring k. It oscillates with a period of 2 seconds when pulled. When an additional 2 kg is add to the block it oscillates with a new period of 3 seconds. What is the mass of the black and the spring constant K?

Homework Equations

T = 2pi*sqrt (m+2/k) my apologies for the format. The symbols will not post for some reason.

The Attempt at a Solution

I attempted to use the about equation above and solve for m. Of course I ran into the problem that I do not know the spring constant k as well. I tried to find K by use the equation and solving for k by imputting the mass of the second block. However I am not confident because the period T at 3 seconds is when the masses are added together and not just for the 2 kg mass alone.

I am fine with the algrebra if I can just start the equation. Any help would be greatly appreciated.

 

[BvU]

You have two values for T, so that's two equations. For two unknowns. A little algebra and both come out just fine !

 

[QuantumKnight]

Thank you for the response. Does this mean I solve both Period equations for k first then solve for mass?

 

[QuantumKnight]

When solving for k: k =(8pi²)/4 = 2pi²
When solving for m: m = ((kT²)/(4pi²)) - 2

 

[lep11]

When solving for k: k =(8pi²)/4 = 2pi²
When solving for m: m = ((kT²)/(4pi²)) - 2

That is not the right way to do this.

You have
T1 = 2pi*sqrt (m/k)
T2= 2pi*sqrt ((m+2)/k)
Now solve both equations for k because k is a constant and don't substitute anything in yet. Then you can set k's equal to each other and solve for m. After knowing the mass of the block you can calculate the spring constant k.

 

[QuantumKnight]

Awesome, thank you