Simple Harmonic Motion

there is something ironic

about motion simple harmonic

a tool to study movements periodic

in the good old Newtonian mechanics

an idealization used with Fourier analysis

to model such complexities

as a pendulum or a bobblehead

and everything that oscillates

all of them movements be

hostage to a force restoring, you see

the force restoring is presumed

proportional to the displacement assumed

and as the name suggests

the force acts to restore the mess

now comes the irony

mentioned in the beginning

if idealized conditions persist

no drag from the air and small displacements that is

the restoring force just never succeeds

inertia conspires to maintain the speed

as the pendulums to the equilibrium reach

a simple harmonic motion forever lives

now, if we talk mathematically

just get to the force restoring fully

and massage the equation so that it is

acceleration and something with displacement in it

equate acceleration to that something, but negative

and you get your motion simple harmonic

if used this trick on a simple pendulum

an insight pops out immediately

that the period of any such system

doesn't quite depend on its energy

it does depend on the string's length

and of course the gravity

swing high swing low a ball of lead or a ball of snow

same time them all will show.