It doesn't keep the same frequency for more than one entire swing, gravity allows it to swing and will eventually make it come to an equilibrium position (come to a stop)
Because when the ball is higher, the vector of the force gravity creates a more perpendicular angle with the line drawn from the ball to the pivot point, this means there is greater torque, and string pivots at a greater speed, and the ball covers a larger distance.
When the ball is lower, the vector force of gravity causes less torque, and the string pivots more slowly and the ball covers a shorter distance. This means that the frequency is the same (at least appears to be) no matter how high the ball is. But as Matt pointed out, the actual frequencies might be slightly different.
Torque = Distance from the Pivot Point X Force, which is a cross product and can be written as
Ï = rFsinÎ where Î is the angle between the rod and the applied force. When theta is 90 degrees (perpendicular), the sine value is the greatest, thus torque is the greatest.
Also consider the fact that the tensional force of the string is greatest when the ball is at the bottom, and 0 when the string is parallel to the ground.
The actual equations are beyond the scope of this question, but can be simplified. If you pull a pendulum farther from its "rest" point, it simply moves faster. A given pendulum will always have the same period and frequency, and this is dependent entirely on its mass and length (technically, the length from the pivot point to its center of mass).
if the mass is moving in a circle, then truly each swing does take a different amount of time. the only way to make a constant frequency is to make the object swing in a cycloid shape.
Comments
It doesn't keep the same frequency for more than one entire swing, gravity allows it to swing and will eventually make it come to an equilibrium position (come to a stop)
Because when the ball is higher, the vector of the force gravity creates a more perpendicular angle with the line drawn from the ball to the pivot point, this means there is greater torque, and string pivots at a greater speed, and the ball covers a larger distance.
When the ball is lower, the vector force of gravity causes less torque, and the string pivots more slowly and the ball covers a shorter distance. This means that the frequency is the same (at least appears to be) no matter how high the ball is. But as Matt pointed out, the actual frequencies might be slightly different.
Torque = Distance from the Pivot Point X Force, which is a cross product and can be written as
Ï = rFsinÎ where Î is the angle between the rod and the applied force. When theta is 90 degrees (perpendicular), the sine value is the greatest, thus torque is the greatest.
Also consider the fact that the tensional force of the string is greatest when the ball is at the bottom, and 0 when the string is parallel to the ground.
Physics.
The actual equations are beyond the scope of this question, but can be simplified. If you pull a pendulum farther from its "rest" point, it simply moves faster. A given pendulum will always have the same period and frequency, and this is dependent entirely on its mass and length (technically, the length from the pivot point to its center of mass).
although a pendulum is only approximately harmonic
it is close enough for small swings
in harmonic motion the restoring force and acceleration are proportional to the displacement
so
the speed is proportional to the distance traveled in a swing
therefore, the time for each swing is the same even as they become shorter and shorter
if the mass is moving in a circle, then truly each swing does take a different amount of time. the only way to make a constant frequency is to make the object swing in a cycloid shape.