Let be the length of the string. Then
implies that which implies that Thus, So, we need to find and as functions of . For , this can be done by equating the kinetic energy that the mass has when its angle is to the change in the mass's potential energy between its initial position and its position when its angle is : Thus, In order to find , we use Lagrange's equation The kinetic energy of the particle is The potential energy of the particle is Therefore the Lagrangian of the particle is Using Langrange's equation, we find that Plugging equations (3) and (4) into equation (1)-(2) gives or Therefore, answer (E) is correct. |

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