Calculating quantities with regards to a pendulum

Question

The set up is a pendulum of length 2m with a mass on the end at 0.5kg. The mass is released at a small initial angle of 6 degrees moving into harmonic motion.

I need to calculate the angular frequency of the oscillations and the maximum velocity then I need to know how the velocity changes if the mass is doubled to 1kg or if the rope length was doubled to 4m.

I need to know how to calculate angular frequency and maximum velocity but then it would be nice if a change in the mass or rope length has a corresponding change in the maximum velocity. If it does, please say but if it doesn't then don't answer that part, I will calculate those myself if you explain how.

Answer 1

Have a look at this page http://arachnoid.com/gravitation_equations/pendulum.html.

The mass has no effect on the pendulum its motion is dependent on the length (L) and the acceleration due to gravity (g).

Answer 2

Hint:

use the conservation of energy, noting that the kinetic energy is $E_k=\frac{1}{2}mv^2$ and the variation of the potential energy is $\Delta E_p=mgl-mgl\cos \theta$ where $\theta$ is the displacement angle.

So you can see that the maximum velocity does not depend from the mass, but it is proportional to the square root of the lenght $l$.