How Does Gravity Affect the Oscillation Period of a Spring?

[kinetix]

Homework Statement

"A certain spring with the mass of 10kg oscillates with a period of 10 seconds on the earth. What would be its period on a small moon, where the gravity is 1/16 as strong as on the earth?"

Homework Equations

I'm thinking I have to use the equation: T=1/2(pi)sqrt[L/g(1/16)]
but I am not sure as my professor will not answer a straight question of 'what formula should I use for this'.

The Attempt at a Solution

I ran into a problem here because the previous question asked almost the same thing but it was speaking of pendulums. I read somewhere that the mass of the spring is irrelevant in this problem but this is just confusing to me. I am only 2 weeks into this course about waves so I haven't had the time to adapt yet.
All help and suggestions are appreciated!
Thank You!
P. Ramos

 

[Delphi51]

That formula for the period looks like the one for a pendulum, not a spring. But I think you have 1/2 where you should have 2.

You can find spring formulas at http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html#c1
I see they give the formula for omega, which is 2(pi)f, and the frequency f is 1/period.
The spring constant k is a measure of how stiff the spring is.

The pendulum and the spring are quite different because gravity is the restoring force that pulls a pendulum back from the extremities of its oscillation. In the case of the spring, it is the spring itself that pulls its mass load back toward the equilibrium position.

 

[tomcue]

I would suggest that you use the formula for the period of a simple harmonic oscillator: T=2π√(m/k), where m is the mass of the object and k is the spring constant. In this case, the mass of the spring is not relevant, but the mass of the object attached to the spring is. Therefore, the period on the small moon would be T=2π√(10/16k), where k is the spring constant on the small moon. This can be calculated by using the formula for the spring constant, k=mg/x, where m is the mass of the object, g is the acceleration due to gravity on the small moon, and x is the displacement of the spring when the object is attached. I hope this helps!