Question

2.a: Consider the differential equation y with the energy V(y, z) = (y +2) / 2. Show that this V(y, z) is conserved. Hint: what is V'? b: Now consider the variant 11 -y-2z with the same energy V(y, z) = (y + z2)/2. Show that this system loses energy. Hint: perfect squares are positive. UO cnocies

please solve this questions for me. Both a) and b) for question 2

Answer 1

2 C 2- 2. zityvlyz) 2y2 2 con served So potenthal for seund case v)yz z49-29 2 . 2- 2. 2 2 = y4z3 2 VCyz)+ 4yz.

y= 2z-z'= -2y'- z! v)=vl)+y v(y)+yy 8y2 vly6y1 yz' < VC42) sytem loses enerjy v' So