How Do You Calculate Mass and Spring Constant from Oscillation Period Changes?

[izmeh]

In a lab write up, i am given the following problem.

An unkown mass M is found to have a period of oscillation of 1 second using a spring of unkown spring constant K. When 200gms were added to the initial mass, the period of oscillation increased by 0.6 seconds. Determin the unkwon mass M(gms) and the Spring Constant K(N/m).

I am not very good at working with problems that have 2 variables. I have come up with a formula however.

T=2pi(sq.rt[M/K])
1 = 2pi(sq.rt[M/K])
1.6 = 2pi(sq.rt[m+.2]/K]
1/1.6 = sq.rt[m/m+.2]

however, i can not for the life of me figure out how to get the answer for M for this.

Is anyone willing to help me?

 

[gnome]

square both sides & solve for m

 

[izmeh]

m cancels out

 

[gnome]

Try it again. It doesn't cancel out.

You're now starting from this line right?
1/1.6 = sq.rt[m/m+.2]
How can m cancel out? When you square it, the right side becomes m/(m+.2).

(If you still can't get it, post what you're doing so we can find the error.)

 

[izmeh]

.625² = sq.rt[m/m+.2]
.391 = m/m+0.2
.391(m+.2) = M
.391m + .078 = m

and so on...

 

[gnome]

Yes, so?

Now you have a simple linear equation for m. There's no way that m cancels out. Finish it & you'll have your solution.