# Period and frequency of a pendulum doesn't depend on mass?

1. Jul 28, 2011

### gkangelexa

Period and frequency of a pendulum doesn't depend on mass??

for a pendulum:

T = 2$\pi$$\sqrt{}length/g$

and f = 1/2$\pi$ $\sqrt{}g/length$

The mass m of the pendulum bob doesn't appear in the formulas for T and f of a pendulum
where T = period
and f = frequency

How does this make sense? If you use a force to push a light child on a swing and use the same force to push a heavy child on a similar swing, the light child should swing faster, right?

bc F = mass x acceleration ... so the one with the lighter mass should accelerate faster therefore its frequency should be higher...?

but according to those equations, the mass doesn't play a role... why?/ how?

2. Jul 28, 2011

Staff Emeritus
Re: Period and frequency of a pendulum doesn't depend on mass??

The more a pendulum weighs, the higher the force it feels. But the more a pendulum weighs, the higher the force needed for a given acceleration. These two effects exactly cancel.

3. Jul 28, 2011

### xts

Re: Period and frequency of a pendulum doesn't depend on mass??

Quick lesson on TeX : $f = \frac{1}{2\pi}\sqrt{\frac{g}{l}}$

Light child would swing faster and with higher acceleration, but frequency will be the same - higher force/acceleration/velocity results with higher amplitude of oscillations, but the frequency remains the same.

Take Galileo's-like thought experiment: two identical penduli, oscillating side by side with another. Now put a drop of glue between iron balls - now you have one pendulum of twice bigger mass. Should this drop of glue change their frequency???

4. Jul 28, 2011

### gkangelexa

Re: Period and frequency of a pendulum doesn't depend on mass??

(wow how did you make that in fraction form? haha)

Conceptually, it makes sense to me that their frequency should change too.... but according to the equation it doesnt change...

5. Jul 28, 2011

### HallsofIvy

Re: Period and frequency of a pendulum doesn't depend on mass??

Well, your concept is wrong! As xts said, if you apply the same force to a lighter child (or pendulum bob) you will give that child a greater acceleration so it will move faster. But that faster speed will result in the child going further. The speed will be greater but the distance traveled will be greater with the net result being that the time taken to travel is constant. The fact that the greater distance traveled at that greater speed is exactly enough to keep the time constant comes from the "conservation of energy".

6. Jul 28, 2011

### rcgldr

Re: Period and frequency of a pendulum doesn't depend on mass??

The swept angle does affect the time, but not by much until the angle gets large. Wiki article with formulas. Although the article mentions θ in units of degrees, in the infinite series formula, θ is in radians.

http://en.wikipedia.org/wiki/Pendulum

7. Jul 28, 2011

### gkangelexa

Re: Period and frequency of a pendulum doesn't depend on mass??

I think i understand your explanation the best. thanks!

8. Jul 28, 2011