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(Solved): 2.26. A double Atwood pulley system consists of three masses and two frictionless, massless pulley ...


2.26. A double Atwood pulley system consists of three masses and two frictionless, massless pulleys (Fig. P2.26). Use the Lag

2.26. A double Atwood pulley system consists of three masses and two frictionless, massless pulleys (Fig. P2.26). Use the Lagrangian method to find the tensions in the cables.


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Given, A double Atwood pulley system.

For the given problem the masses of pulley and cables are negligible.The double machine is an Atwood machine in which one of the weights is replaced by a second Atwwod machine. The system now has two degrees of freedom and its its instantaneous configuration is specified by two coordinates   .

   are two coordinates,    denotes the length of the vertical parts of the two strings.


The total kinetic energy of the system can be expressed as:
  
The total potential energy of the system: Considering
  
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