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Q. use d'alemberts principal to find the condition of static equilibrium

so

i prolly want to look at the coordinates of the system with respect to theta

x = L sin Theta where L is the length of the string

y = - L cos theta

(Fapplied - Finertial) delta r = 0

Im guessing the F applied is both the horizontal force and the force of gravity

and that the inertial force is m * L * theta (double dot)

delta r = L * delta theta

so im just wildly guessing that

(Fapplied - Finertial) delta r = 0

(Fsin theta + mg cos theta - m * L * theta (double dot) ) delta r = 0

i know im wrong but maybe someone can tell me what im doing wrong