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Distinguish between the following approaches for solving problems. The method of applying Newton's second law from the Lagrangean method. [5] 2.12 22 The method of applying the Lagrangean from the Hamiltonian method. [4] A simple pendulum consists of a particle of mass m on an inextensible massless string of length The kinetic energy of the system in Cartesian coordinates is given by: Tam (x2 + y2) wherex and y may also be expressed in their polar coordinates format asx = £ sin 0, and y=-& cos O respectively. 2.2.1 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. Lame202 + mgl cos e [5] State the number of degrees of freedom and the number (name them also) of the generalised coordinates of the system? [3] 2.2.3 From the Euler-Lagrange equation of motion: 222 az ƏL = 0, dt 'aak da Show that the equation of motion for this system is given by: Ö + 0 = 0 What can you conclude about the system from this equation of motion? [6] [2]