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## Homework Statement

a pendulum of mass m and length L is pulled back an angle θ and released. After the pendulum swings through its lowest point, it encounters a peg α degrees out and r meters from the top of the string. The mass swings up about the peg until the string becomes slack with the mass falling inward and hitting the peg. show that cosθ=r/Lcosα-√3/2(1-r/L)

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## The Attempt at a Solution

I tried to find the forces on the pendulum at the initial and final position

Lcosθ-mg=0

Lsinθ=ma

rcosθ-mg=0

rsinθ=ma

but it doesn't seem to work at all. what I get is that r=L which is impossible.