How you find the oscillation period of a mass if not given the mass, or spring constant?

Question: A mass is attached to a vertical spring, which then goes into oscillation. At the high point of the oscillation, the spring is in the original unstretched equilibrium position it had before the mass was attached; the low point is 3.7cm below this. Find the oscillation period, T.

Question

How you find the oscillation period of a mass if not given the mass, or spring constant? 

Question: A mass is attached to a vertical spring, which then goes into oscillation. At the high point of the oscillation, the spring is in the original unstretched equilibrium position it had before the mass was attached; the low point is 3.7cm below this. Find the oscillation period, T.

theeric · Answer

Hmm.. If I had to make a wild guess as to what makes this special, it's that the high point of the oscillation is the same point at which the spring reaches unstretched!

theeric · Answer

That means that

the amplitude displaces the mass
just as much as
the weight stretches the spring.

That might give us a "constraint," a relationship that we can use to constrain the general equation to one that meets our specific circumstance.

And hopefully mass and spring constant unknowns cancel, later.

theeric · Answer

Do you have any thoughts?

theeric · Answer

$A=x$
$kx=mg\quad\implies\quad x=g\dfrac m k$
$A=g\dfrac m k$

Double check that. Does that help?

And we are given twice the amplitude. Look for that, and that will help. Draw a picture if you need more help!