## College Physics (4th Edition)

The correct answer is: (a) $T_A = T_B$ and $E_A \gt E_B$
We can write the equation for the period of a pendulum: $T = 2\pi~\sqrt{\frac{L}{g}}$ Since both pendulums have the same length, the period of each pendulum is equal. Since the amplitude is equal and the length is equal, the change in height $h$ between the lowest point and the highest point is the same for each pendulum. The energy in the pendulum can be expressed as $mgh$. Since the mass of A is larger, then the energy of A is larger. The correct answer is: (a) $T_A = T_B$ and $E_A \gt E_B$