Consider the temperature distribution in a thin circular ring. Assume the external sur- faces being perfectly insulated, and the ring is thin enough so that the temperature does not vary with distance from the center of the ring. The diagram below is constructed with 36 as the arc length of the ring measured from the lowest point: x = 1,x = 1 x=0 The initial temperature distribution of this ring is f(x). Considering x = 1 and x = 1 being the same point on this ring, solve this using 1D heat equation. [A1153 \"(37715) = 3* + Z A; COS mm e_("c\")2t + 0;: sin mm e_("c\")2t "=1 n=1 where B* = if: f(x) dx, A; 2 L11 f(x) cos mm dx 0,"; = L11 f(x) sinmrx dx]