A mass is attached to a pendulum of length L that is at an angle theta (8) with respect to the normal. The mass has an initial velocity Vo. What is the minimum speed (symbolically) needed for the mass to go all the way down to its lowest point and all the way back up its highest point (as in, the rope of the pendulum is projected vertically upwards). I set 1/2(m)Vo^2 + mgL(1-cos(8)) = 2mgL and got Vo = square root of 2gL + 2gLcos(8), but my book says it is the square root of 3gL + 2gLcos(8). I don't see what's wrong with my set up, as I have checked the result of this set up several times and got the same answer.