S36Consider two blocks of masses mi and m; attached together with a massless and un-stretchablestring of constant length L. The string passes over a small, massless and frictionless pulley. Thed or cremass mi is heavier than m:, the direction of motion is presented in the figure below. Take thes dorgravitational potential energy PE = 0 at the level of pulley. Neglect all frietion effects and theradius of the pulley. Take x, = -X,y =0, ==0,y:=0 and z;= 0.(a) Write down the constraint relation(s).(b) Show that the number s of degrees of freedom is 1.(c) Obtain expressions for the kinetic energy, potential energy,commT comLagrangian as a function of x, and x,PEco(d) Write the equation the equation of generalized momenta Pat.(e) Deduce the Hamiltonian as a function of Pa1, X1, g, m; and m2.() Use the Hamilton canonical equations and determine the equation of motionof the two blocks(2) Deduce the expression of the accelerations , as a function of m, and m; and thegravity.

More than three subparts are required to be solved, so the 1st three has been solved. The Total…

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