Angular SHM and Simple Pendulum: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Angular SHM and Simple Pendulum. Understanding the underlying formula is key to arriving at the correct answer below:

Time period $ T \propto \sqrt{l} $. $ \frac{T_1}{T_2} = \sqrt{\frac{2}{0.5}} = 2 $, so $ T_1 = 2T_2 $. They return to the same phase when the longer pendulum completes 1 oscillation and the shorter one completes 2 oscillations.