Question 5. A light balloon that has a volume 2.50 m filled with a helium (pHe = 0.179 kg/m") is tied to a light string of length L = 5.50 m. The string is tied to the ground, forming an "inverted" simple pendulum, as in Figure 2a. If the balloon is displaced slightly from the equilibrium position, as in Figure 2b (Pair = 1.29 kg/m3). Determine a) the spring constant, k, (5 marks) (Hint : Use an analogy with the mass hanging at the end of a spring. Solve for the value of k assuming that the restoring force acting on the system takes the same form as Hooke's law), b) the time period of its simple harmonic motion, (3 marks) c) the frequency of the simple harmonic motion. (2 marks) He Air Air He L. Figure 2: Inverted Pendulum for Question 5