The formula for the period of a pendulum (i.e. the timing) includes only the length (shoulder to hand) as a variable, the mass of the object has no effect on the timing.
Related is the test performed on the moon, where an astronaut dropped a hammer and a feather from the same height, and they both landed at the same time.
If mass nor gravity have an effect on a pendulum, then why do they eventually quit swinging? Mass according to physics, is a quantity of matter as determined from it's weight. An object in motion tends to stay in motion but for how long? What unseen force over time causes that object to cease motion? Gravity. That one little thing the moon has very little of that Earth has in abundance. So on Earth, the mass does have an effect on timing. Otherwise clock makers would have been able to use any size, shape and weight object at the end of the pendulum to make grandfather clocks and their miniature clones.
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The "unseen" force that causes an object to cease motion is called friction. Both in the "shoulder" and in the air.
The moon has 1/6th the gravity of the earth, the big difference is a lack of atmosphere. No air friction allowed the feather to fall at full acceleration, and keep up with the hammer.
A sky diver will accelerate towards the earth until reaching terminal velocity. That's when the force down due to gravity and the force up due to air friction match.
If you look at a grandfather clock there is usually a little adjuster knob at the bottom of the pendulum, it moves the weight up or down the arm effectively shortening or lengthening the "arm"
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