Serway & Jewett — Oscillatory Motion: Problem 46

Review. A light balloon filled with helium of density \( 0.179 \text{ kg/m}^3 \) is tied to a light string of length \( L = 3.00 \text{ m} \). The string is tied to the ground forming an “inverted” simple pendulum (Fig. P15.46a). If the balloon is displaced slightly from equilibrium as in Figure P15.46b and released, (a) show that the motion is simple harmonic and (b) determine the period of the motion. Take the density of air to be \( 1.20 \text{ kg/m}^3 \). Hint: Use an analogy with the simple pendulum and see Chapter 14. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.