How
to lose weight

Pedro
Hugo García Peláez

Dedicado
a mi madre, con todo el cariño, allí donde quiera que esté

All
rights reserved. No part of this publication may be reproduced,
distributed, or transmitted in any form or by any means, including
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without the prior written permission of the publisher, except in the
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requests, write to the publisher at the e-mail below.

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©
Pedro Hugo García Peláez, 2016

Prologue:

When
I wrote this book. I thought it was not necessary to introduce
complicated concepts such as differential equations, to justify the
formula for the period of flotation of a body of square symmetry, or
the equation of a simple harmonic motion because that would be
subject of a physic book.

Perhaps
some of my readers know the concept of derivative in mathematics, but
if I also write the resolution of a differential equation probably
they get bored and what I want is to reach all the public like a
housewife, a professional of anything or a grandfather who is at
home, whether they have college degrees or not.

Therefore,
I have written a book based on physic science that can be read by
everyone with a simple and clear language

The
hardest thing you will have to solve is a square root. Things like
root of nine equals three because three by three is nine.

With
the help of calculators is not a problem.

`Swimming resonance effects`

I
have a phrase:

"What
cannot be measured is not useful".

This
book gives you the characteristic time which you must swim depending
on the characteristics of your own body.

In
a simple system, obviously the mechanism is simpler because the
pendulum resonates with itself, or your arm when moving in its
natural frequency period resonates with itself, but even if they are
simple systems for all purposes you are taking advantage of that
amplitude which tends to infinity, as in the case of the soprano who
breaks the cup with her voice.

It
is the natural frequency of oscillation of the house.

It
is the frequency of the earthquake that made the earth vibrate.

We
have seen that when entering resonance the amplitude increases
considerably, a small earthquake can bring down a house if both
systems enter in resonance

Another
simple system would be a body of square symmetry floating into the
water that begins to move up and down in the water, this is again a
(m.a.s) as in the case of a pendulum. Only that the body of square
symmetry now oscillates up and down in the
water with a characteristic
time, as in the case of a pendulum that have his own characteristic
time of oscillation.

### Simple harmonic motion = (m.a.s)

A
few years ago an idea came out of the sky. It was September ... In
January I had an exam of mechanics and waves. I spent the day doing
problems, such was the skill he was having with the problems that
almost intuited new variables. I practically dominated the exercises
of my book, the truth is that I went to bed exhausted.

One
morning when I woke up

I
had an idea that could simplify calculations of how a human being
should swim.

I
do not know if the idea came to me by divine inspiration or because
the enormous work that was being carried out by solving the problems.

The
idea was to liken the human body to a body of square symmetry, when
we float in the water without moving the human body is quite similar
to a body of square symmetry.

It
was November and the next day went to a Spa in Madrid, after
measuring my natural frequency of floating, and then saw that fat
accumulated in the stomach disappeared almost instantly, it was like
putting the stomach in a centrifuge.

If
we apply a vertical force on a body of square symmetry floating in
the water, the body will go up and down in their own characteristic
time also does not matter if we sink much or little that will do the
path at the same time, obviously if we sink deeper will travel up and
down faster since it must cover more space at the same time, this is
an important feature, the amplitude that is the distance traveled is
independent of its typical period.

Also,
in the water there is less friction and the invention worked. A
square body symmetry has the same natural oscillation period of a
boat of square sides, like a tanker.

The
formula is: 2 * π * the square root of the weighted average of our
side, divided by the square root of the acceleration of gravity that
is 9.81
m/s₂

This
formula is
exact as the formula of a simple pendulum, now the length of the rope
is the width of our own human side if we consider our body as a
floating body of square symmetry.

It
comes because the (m.a.s) of a floating body is connected with the
circular motion, we all remember the formula of the length of a
circumference, which is:

(g)
is the acceleration of gravity on earth and comes after of simplify
the weight of the swimmer and the urging force of the dislodged
water, or Archimede´s principle.

And
the variable width of human is because you have to take into account
the density of the liquid, which is its mass divided by its volume,
in the case of water is close to 1 kilogram per cubic meter, much
like the human density.

This
is the cause that allows us to float on water.

And
here comes the variable width of the sides that without this variable
all men, boats, etc. would the same period of natural buoyancy.

We
see that in the formula of natural oscillation of a body of square
symmetry in the water, there is only one variable, so we can simplify
and remains that:

Therefore,
we multiply the square root of the weighted average width of our
human side by 2 to find our natural floating period in seconds.

A
weighted average is an estimate of different measures of the same
body, for example in our chest the width it is greater than in our
ankles, the thighs are wider than the ankles, but less than our
chest.

Moreover
we are considering that:

(g)
The acceleration of gravity is constant in all parts of the planet,
unless you do the exercise in a pool at the peak of the Himalaya, and
on the other hand is the (g) characteristic of Planet Earth, if you
did in a pool at The Moon, have another (g) since in The Moon force
of gravity is lower.

What
we get with this? in principle two things, enter in phase with the
force of gravity and the range of motion tends to infinity.

Thus
we see that more obese person must swim more slowly because the
variable of the human side is in the numerator and it makes longer
period, and therefore must make full movement in longer and therefore
more slowly.

The
period is the time in which the body must be in the same situation
after going down and go up on the water.

If
you do a weighted average of the human side it comes to be about 14
cm. (wider in the thighs, thinner in the ankles and most wider in the
stomach).

*
1 inch = 0,0254 meters

Measuring
this variable in your body, you can already measure the time in which
you must make a swimming stroke, in the case of a side with an
average width of 0.14 meters the period is 0.75 seconds.

This
is the time when we must make a swimming stroke, (since we started to
immerse ourselves and we back again to be in the same position).

Thus
we get the strength to develop this movement to get into resonance
with the natural frequency of our own body to float.

It
is curious that this time approaches to one second that is the time
unit of the international system of measures.

The
period of floating of a human being, generally ranges between 0.6 and
1 second, depending on whether the person is thin or obese.

Although
it is best done in a large pool or in the sea, swimming 1/2 minute
resting and returning to swim a total of about 10 minutes, about two
or three times a week also can be done in a small pool without much
swin advance, though results are much less spectacular. So it can be
done in a small pool, but I repeat that the results are much less
spectacular.

If
you want to see otherwise, your body should get to swim following a
sine function of period 0.75 seconds.

We
see that the position of the swimmer is repeated each certain time
that is the period or time in which we make a swimming stroke.

It
really is in the vertical movement up and down the swimmer where
(m.a.s) occurs.

I
have also tried at sea and the results are the same, but resonate at
a time with the waves is another story because they have their own
natural frequency, and it is difficult for two physical oscillators
go into resonance (our body floating and the natural frequency of
waves).

You
should measure the period of the waves, which near the beach have a
fairly constant period, if the oscillation period is about one second
the approximation would be excellent, one second from start to form
near the coast goes up and down until they disappear.

In
this case we should swim perpendicular to the coast to take advantage
of the rise and fall of the waves, although it should be about a
second to take advantage of waves.

I
repeat that the movement should be parallel to the coast, not
perpendicular as do the surfers to harness their push because that is
another story.

We
see that the same formula for measuring the period of oscillation of
a pendulum is used, and to measure the flotation period of a body
similar like a square table

In
a simple pendulum (h) is the string length, and in the case of
swimming body (h) is the average width of our human side.

Finally
consider that the human body is not like a square table, but an
approximation of 80% is good enough in physics approximations are
used continuously in many cases, as greatly simplify the
calculations, and often are perfectly valid to solve problems that we
face.

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