POEM OF WAVES

WAVES:

Congratulations!

Today is your day.
You’re off to learn many
Great things about waves!

You have math in your brains.
You have waves all around.
And soon you will find
That oscillations abound.
You’re not on you own if you know what I know.
But YOU are the one who’ll learn how these waves go.

Waves go up and down sine curves, so graph them with care
Though sometimes equations make life less hard to bear.
F equals ma helps you find diff. EQ’s
And select t of zero so phi you will lose.

Simple harmonics are the
Pulse of all things.
We study them using
Complex numbers, and springs!

But springiness changes
If life rearranges…

With damping and driving
The amplitude GROWS
If the frequency to
Omega-s goes.

And when resonance happens,
Don’t worry. Don’t stew.
Just know that the max
Is related to Q.

OH! THE PLACES WAVES GO!

Oscillations in springs
And on strings and of light!
With such simple motions,
The waves can take flight!

They don’t lag behind if you add a phase shift:
Delta, we call it, is pi-over-two
Whenever the drive frequency is the square root
Of k-over-m, (omega-s, to you).
But if it isn’t
Then delta is different.

I’m sorry to say so
But, sadly, it’s true
That nasty
Equations
Can happen to you.

And amplitude, too,
Of the damped-driven kind,
Is less messy and stress-y
With these things in mind.

Tan delta is gamma
Times drive over both
Frequencies squared-minused.
And you’ll then not be loathe

To find amplitude which
Is not so much fun
And deriving this one
is not easily done.

Soon you’ll come to a place where the springs are combined
With pendulum bobs ¬ it will boggle your mind
And the beats…