A string with a bowling ball tied to its end is attached to the ceiling. The string is pulled back such that
it makes a 10° angle with the vertical, and it is then released. When the bowling ball reaches its lowest
point, it has a speed of 2 m/s. What is the frequency of this bowling ball pendulum?To calculate the period of this pendulum, we must know the length of the string. We can calculate this
using conservation of energy. Then, we’ll convert the period to a frequency.
Before the string is released, all of the bowling ball’s energy is in the form of gravitational PE. If we
define the zero of potential to be at the ball’s lowest point, then at that point all the bowling ball’s energy
is in the form of KE. We will use a subscript “a ” to represent values before the bowling ball is released
and “b ” to represent values when the bowling ball is at its lowest point.
The height of the bowling ball before it is released, ha , can be calculated using trigonometry.
So, getting back to our previous equation, we have