Movement Of String Wave

Today is Thursday, 5th of February 2015.

 

A few days ago, I was wondering about the changes in movement of a wave, especially the mechanical one, for instance the wave created by using a string.

 

Aim of My Attempt

Actually, I intend to perform this experiment as I want to know how this physical string behave when it is transferring energy.

Moreover, the most intriguing phenomena of the wave shown by string is reflection, whereby the wave "bounces off" the surface it contacts.

 

After some pain-stacking attempts, I have managed to capture the motion of the wave in video form.

After studying this wave carefully, I wish that I could find out how this wave actually behaves.

 

For my interpretation:

Below is the real-time video of the wave :
 

 

video above is faster

below is slower

 

 

 

I find out that the wave of the string behave quite funny...

That is, it actually reflect itself by pulling itself on the string and causes half of the wave to be reflected upside down.

I am trying to figure the mathematics behind this wave "model".

 

The motion of the wave :

              _

--------_-  ----->       first step

 

                      _

--------------_-  >      second step

 

 

----------------   >         third step    ( two waves superimposed results in increased amplitude, 2a .

                     |_|

 

                      _

--------------_-  >        forth step

 

                  _

-----------_-  --->        fifth step

 

 

Could the above illustration be true? It still needs further observations to confirm.

                     

 

 

 

 



            The First Doubt that I Firstly Post Online :)

FRIDAY          30 JAN 2015 

{The Motion of a Falling Ball under a Hyperbolical Path}


ABSTRACT
Long time ago, there has been several grand scientists such as Galileo Galelei, Sir Isaac Newton, and many others began to investigate the motion of objects around them. For instance, Galileo Galelei, the first person who made use of the telescope in astronomy had study the motion of the falling objects at the Leaning Tower of Pisa, Italy.

Hereby, being inspired by those scientists, I intend to perform my own so called "scientific experiment", the topic of my study is the "Motion of a Falling Ball under a Hyperbolical Path".

I will try to improve my way of tackling this experiment. :)



Actually, I was wondering how to tackle the mathematical equation, that is to integrate the equation of "inverse" trigonometric function!

Anyway, I plotted a graph of motion of the object and the calculate the area under the graph manually....

Could anyone teach me how to integrate the equation of inverse trigonometric function?