A light balloon filled with helium of density 0.179 kg/m3 is tied to a light string of length L 5 3.00 m. The string is tied to the ground, forming an inverted simple pendulum (Fig. P13.71a). If the balloon is displaced slightly from equilibrium, as in Figure P13.71b, (a) show that the motion is simple harmonic and (b) 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.

Physics 2 for Engineering Week 14 Beats 2 sound waves with slightly different frequencies Tbeat= T a b (T -Tb) and f beat= 1 / Tbeat= f a b Tbeatis time it takes to go from minimum to minimum or maximum to maximum Tbeat= nT =a(n-1) T b Doppler Effect f heard by observer depends on relative motion of the source with respect to the observer f’ = f (vsound+- v observer/ (vsound+- v source Depends on relative motion of source and observer Moving towards each other – higher frequency Moving away from each other – lower frequency f is frequency of sound, and f’ is frequency of sound heard by the observer Source at rest, observer moves towards f’ = f (v s