A hot-air balloon of mass m is used to lift a load, Mg, by means of 12 equally spaced elastic ropes, each of stiffness k (see Fig. 5.60). Find the natural frequencies of vibration of the balloon in vertical direction. State the assumptions made in your solution and discuss their validity.
![1093_460791d0-4c06-4bda-ba61-988bb7e05585.png](https://secure.tutorsglobe.com/CMSImages/1093_460791d0-4c06-4bda-ba61-988bb7e05585.png)