Simple Harmonic Motion of Inverted Simple Pendulum with a Helium Balloon

[Touchme]

Homework Statement

A light balloon filled with helium of density 0.175 kg/m3 is tied to a light string of length L = 3.35 m. The string is tied to the ground, forming an "inverted" simple pendulum (Fig. P13.63a). If the balloon is displaced slightly from equilibrium, as in Figure P13.63b, show that the motion is simple harmonic (do this on paper. Your instructor may ask you to turn in this work), and determine the period of the motion. Take the density of air to be 1.29 kg/m3. (Hint: Use an analogy with the simple pendulum discussed in the text, and see Chapter 9.)

Homework Equations

Ft = [-(density of air - density of He)Vg)/L]s
T= 2pi*sq.root of L/g

The Attempt at a Solution

I tried to play around with the formulas, however, I was unsuccessful. I'm not sure if those formulas are relevant to the question. Any suggestion on how to start solving or any hints?

 

[OlderDan]

Hint: If the balloon were released, what would its acceleration be? I assume you are supposed to neglect the resistance of the air to the motion of the balloon. You can't have the balloon floating without the air, but you can neglect the resistance effect.

 

[Touchme]

The acceleration would be
a = ((d(air) - d(gas))V - m)g/(m + d(gas)V)
So...
I neglected mass but it says a light balloon...
a = (1.29-0.175)(9.8)V/(0.175V)
a=62.44 m/s

Hmmm... then I use the period formula and...
GOT IT!
thanks OlderDan =D