Well, let's see. How do we solve this.
Well, I know that the potential energy over here is going to be equal to the kinetic energy
it has when it passes through the equilibrium.
Remember at the the equilibrium point, there's no potential energy.
All of that energy must have been converted into kinetic energy.
Okay, so let's do the math. Potential energy gets converted to kinetic energy.
Use the appropriate equations and when I solve for V--that should be a max
and I'm solving for the Vmax as well.
I get this for an answer and plugging in the appropriate values--I get an answer of 4.5 m/s.
Now something that's interesting here is that this could've been positive number
or a negative number--a positive number would have corresponded to when the mass
is moving this way and negative would have corresponded to when the mass is moving that way.
In fact, there's a lot we can learn about simple harmonic motion by just calculating velocity,
keeping track of sign and plotting it on a diagram versus position.
What do I mean by that? Well, I'll show you.