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A simple pendulum consists of a particle of mass m on an inextensible massless string of length t. The kinetic energy of the system in Cartesian coordinates is given by: T==m (x2 + y²) where x and y may also be expressed in their polar coordinates %3D I cor A resnectively

A simple pendulum consists of a particle of mass m on an inextensible massless string of length t. The kinetic energy of the system in Cartesian coordinates is given by: T==m (x2 + y²) where x and y may also be expressed in their polar coordinates %3D I cor A resnectively

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3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length l. The kinetic energy of the system in Cartesian coordinates is given by T==m (x2 + y²) where x and y may also be expressed in their polar coordinates format as x = l sin 0, and y = -l cos 0 respectively. 3.2.1 Assuming the origin is located at the point where the string is attached to the support, show that the Lagrangian of the system is given by: + mgł cos e 3.2.2 State the number of degrees of freedom and the number (name them also) of the generalised coordinates of the system?
Transcribed Image Text:3.2 A simple pendulum consists of a particle of mass m on an inextensible massless string of length l. The kinetic energy of the system in Cartesian coordinates is given by T==m (x2 + y²) where x and y may also be expressed in their polar coordinates format as x = l sin 0, and y = -l cos 0 respectively. 3.2.1 Assuming the origin is located at the point where the string is attached to the support, show that the Lagrangian of the system is given by: + mgł cos e 3.2.2 State the number of degrees of freedom and the number (name them also) of the generalised coordinates of the system?
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