(Solved): (a) Consider a body which moves down a plane with friction and such that the ...

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(a) Consider a body which moves down a plane with friction and such that the inclination of the plane varies with time. Justify whether: (i) the constrains are holonomic or non-holonomic; (ii) the constrains are scleronomic or rheonomic; (iii) the system is conservative or dissipative. (b) Given the integral $$I?{?}_{t_1}^{t_2}\left(x^3?{\stackrel{?}{x}}^2+x{t}^2\right)dt,$$ obtain a differential equation for the function $$x(t)$$ which makes the integral $$I$$ extremal.