Problem: A pendulum is formed from a small ball of mass exttip{m}{m} on a string of length exttip{L}{L}. As the figure shows, a peg is height exttip{h}{h} =L/3 above the pendulums lowest point. From what minimum angle exttip{ heta }{theta} must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

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A pendulum is formed from a small ball of mass on a string of length . As the figure shows, a peg is height =L/3 above the pendulums lowest point. A figure shows a pendulum consisting of a ball at the end of a string of length L. A peg is placed at the height of L divided by 3 above the lowest point of the pendulum. When the ball reaches and passes this peg, it swings upward as a pendulum with the string length of L divided by 3.

From what minimum angle must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?