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 doesnt effect the time period?