Restoring Force- any suggestions?

[bcjochim07]

Homework Statement

An object of mass m is connected between two stretched rubber bands of length L. The object rests on a frictionless surface. At equilibrium, the tension in each rubber band is T. Find an expression for the freq. of the oscillations perpendicular to the rubber bands. Assume the amplitude is sufficiently small that the magnitude of the tension remains essentially unchanged.

Homework Equations

The Attempt at a Solution

Here's what I tried, but I have no idea if it's right.

I drew a picture, and found that as it oscillates, the tension in each rubber band in the direction perpendicular to the rubber bands is Tsintheta. Using the small angle approximation, I come up with T(d/L) Where d is the distance perpendicular from the original position of the mass. So the total restoring force is 2T(d/L)

and then I set that equal to the restoring force with the spring constant

2T(d/L)=kd and came up with an expression for k and then substuted that into the frequency equation. Any suggestions?

 

[lzkelley]

your method is completely correct.
Because its simple harmonic motion (i.e. no damping or forcing) all you need to know is the mass (given) and the force - which you found, and looks right.