A ball attached to a string length `L` is oscillating line a simple pendulum. Find `v` in terms of `v_0` `L` `alpha` and `beta`.

Explanation

`K_1=(1)/(2)mv_0^2`,`U_1=-mgLcosalpha`
`K_2=(1)/(2)mv^2`,`U_2=-mgLcosbeta`
`K_1+U_1=K_2+U_2`
`(1)/(2)mv_0^2-mgLcosalpha=(1)/(2)mv^2-mgLcosbeta`
`v=sqrt(v_0^2+2gL(cosbeta-cosalpha))`

If we assume the reference line at (2), then
`K_1=(1)/(2)mv_0^2`,`U_1=mgL(cosbeta-cosalpha)`
`K_2=(1)/(2)mv^2`,`U_2=0`