Why doesn't mass of a pendulum effect its time period

[Revin]

I'll jump straight to my query.

If PE = mgh, and if the "m" is increased, the PE shall also increase.
Neglecting friction, Total mechanical energy(TME) = PE + KE.
Since PE increases, the total mechanical energy of the system shall also increase.
At its equilibrium position, where PE = 0, it should have a greater amount of KE since
KE = TME-PE.

Having more kinetic energy, it should hence have more velocity as well.
Hence, having more velocity, its time period should be shortened since it takes lesser time for it to complete one oscillation having the same distance ( Note that the value of h is not changed here).

After all this, why is it practically proven that mass doesn't effect the time period?

 

[UltrafastPED]

See http://www.Newton.dep.anl.gov/askasci/phy05/phy05214.htm

 

[DrGreg]

If PE = mgh, and if the "m" is increased, the PE shall also increase.
Neglecting friction, Total mechanical energy(TME) = PE + KE.
Since PE increases, the total mechanical energy of the system shall also increase.
At its equilibrium position, where PE = 0, it should have a greater amount of KE since
KE = TME-PE.

OK so far.

Having more kinetic energy, it should hence have more velocity as well.

No. Kinetic energy doesn't just depend on velocity, it depends on something else as well...

 

[Buckleymanor]

All masses fall at the same rate.In effect your pendulum is a falling mass with just the right amount of added energy from the mechanism to overcome friction if it's in a clock so it does not stop.
If it's just a pendulum then it's a falling mass on a rope when it swings.
And all masses swing or fall at the same rate within a gravity field.

 

[sophiecentaur]

Dear old Galileo sorted this out a long time ago. The story is that he won a bet about dropping masses off the Tower of Pisa. His contemporaries believed that a heavy object would reach the bottom before a light object - he knew better. That's just a story but is shows that reality is often counter-intuitive.