[Verse 1]
I want to talk today about things that shake
And I hope my words aren't too opaque
One degree of freedom moving to and fro
Just how it moves, we’d like to know
We can represent all kinds of things
By a single mass between ideal springs
Each spring's connected to a wall
So the outer ends don't move at all
[Verse 2]
Let the mass be m, spring constant k
But don’t let friction get in the way
Use Newton's Laws, and what do we got?
F equals m psi double dot
F is also minus k psi times two
So now we have a diff E Q
And we can write down the general solution
For the simple harmonic time evolution
[Verse 3]
Let omega be root two k over m
Here's the answer. Won't repeat again
Psi is A cosine omega
Plus a phase, call it phi
So it's all very simple. And you can see
For any initial psi and velocity
We can find the constants A and phi
And the equation's exact for all time t
I want to talk today about things that shake
And I hope my words aren't too opaque
One degree of freedom moving to and fro
Just how it moves, we’d like to know
We can represent all kinds of things
By a single mass between ideal springs
Each spring's connected to a wall
So the outer ends don't move at all
[Verse 2]
Let the mass be m, spring constant k
But don’t let friction get in the way
Use Newton's Laws, and what do we got?
F equals m psi double dot
F is also minus k psi times two
So now we have a diff E Q
And we can write down the general solution
For the simple harmonic time evolution
[Verse 3]
Let omega be root two k over m
Here's the answer. Won't repeat again
Psi is A cosine omega
Plus a phase, call it phi
So it's all very simple. And you can see
For any initial psi and velocity
We can find the constants A and phi
And the equation's exact for all time t
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