MHB Max Velocity of a Pendulum Released from Rest

[Dustinsfl]

A pendulum is released from rest at a distance y = H for the y = 0.

What is the max velocity?
\[
\frac{1}{2}mv^2 = mgh\Rightarrow v = \sqrt{2gh}
\]
where I assumed there was no air resistance.

Would anything change if the system was in a vacuum?

 

[alexmahone]

Re: pendulum

Looks right to me.

Assuming that there is no air resistance is equivalent to assuming that the system is in a vacuum.

 

[Dustinsfl]

Re: pendulum

Now suppose the first mass has elastic collision with a second mass hanging at equilibrium.
I have solved for the final velocities using CoM and CoKE but can it be simplifies any further is what I am wondering.
\begin{align}
v_1^f &= v_2^f - \sqrt{2gh}\\
v_2^f &= \sqrt{2gh} + v_1^f
\end{align}