What is the minimum horizontal force "F" required to hold a simple pendulum (mass "m") with string of length "l" at an angle of 60 degrees with the vertical. [ given answer = mg/√(3) , veracity uncertain ] This at first seemed simple enough, standard mechanics apply, leading to : F/mg = tan(θ) where "θ" is the angle of the string from the vertical here: F/mg = tan(60) F = mg√(3) My second attempt, using the Law of Conservation of Energy, lead to this : Taking "mean" position of pendulum as the Origin and Assuming that bob is brought up - Final ( KE + PE ) (of bob) = Initial ( KE + PE ) + Work done on bob mgl(1-cos(60)) = 0 + Work done by Tension + Work done by F mgl(1-cos(60)) = 0 + 0 + F (l sin(60)) mgl/2 = Fl √(3)/2 F = mg/√(3) huh. Why would they give different solutions? I am assuming I did something wrong. I apologize if it is hard to understand, I have trouble conveying it without a diagram.