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## Homework Statement

A light balloon filled with helium of density 0.18 kg/[itex]m^{3}[/itex] is tied to a light string of length 1.51 m. The string is tied to the ground, forming an “inverted” simple pendulum as in the figure. The acceleration of gravity is 9.8 m/[itex]s^{2}[/itex]. If the balloon is displaced slightly from equilibrium, find the period of the motion. Take the density of air to be 1.29 kg/[itex]m^{3}[/itex]. Answer in units of s.

## Homework Equations

T = 2[itex]\pi[/itex][itex]\sqrt{m/k}[/itex]

Fb = ρVg

## The Attempt at a Solution

I know Archimede's principle and SHM apply here, but I cannot make the connection. Can anyone take me step by step please?