A pendulum is made of a massless string of length \( L \) and a small bob of negligible size and mass \( m \). It is released making an angle \( \theta_0 \) (<< 1 rad) from the vertical. When passing through the vertical, the string slips a bit from the pivot so that its length increases by a small amount \( \delta \) (\( \delta \ll L \)) in negligible time. If it swings up to angle \( \theta_1 \) on the other side before starting to swing back, then to a good approximation, which of the following expressions is correct?
