What is the natural frequency for a child's swing with 2.00 m long chains?

[CactuarEnigma]

Please help me with this, it's one of the 'basic' problems and I can't do it at all. "The chains suspending a child's swing are 2.00 m long. At what frequency should a big brother push to make the child swing with largest amplitude?"

Okay, so... the largest amplitude comes with a natural frequency...
f1 = (1/2L)*(T/mu)^(1/2)

I'm trying to figgure out why the rooted part gets to (g/L)^1/2... if T is mg and mu is m/L, wouldn't it be (gL)^1/2? And how does 1/2L turn into 1/2pi? Thanks for any help you can offer.

 

[Päällikkö]

You are using a formula for transverse waves.

With the small angle approximation, the period of a pendulum:
$$T = 2\pi \sqrt{\frac{l}{g}}$$