Undergrad Effect of Nearby Mountain on an Ideal Pendulum

[bob012345]

Suppose there is a very large mountain adjacent to a pendulum such that there is a horizontal component gravitational force of $10^{-5}g$ acting on the otherwise ideal pendulum. How would one use a perturbation to add that effect to first order?

My initial thought would be to figure an angle that made the total gravitational acceleration ##g(-1z+10^{−5}x)## operating around a symmetric axis and which gives an ideal pendulum and then transform the coordinates?

 

[.Scott]

If you are only looking for a 1st order approximation, treat it as a 1g pendulum with the center of the swing displaced 10^-5 A were A is the length of the pendulum arm.