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HPS250H1 Lecture : 23rd Jan 2012.doc

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School
UTSG
Department
History and Philosophy of Science and Technology
Course
HPS250H1
Professor
Hakob Barseghyan

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Document Summary

Only absolutely certain propositions (theorems) are then deduced from the axioms. Synthetic propositions and analytic propositions are what distinguish the formal sciences and the empirical sciences. A: you try to conceive of a world where it is not a case (the opposite) If you can do so, then iti s synthetic. The opposite of a priori is a postiori (aka. Eg. matter has 2 attributes: extension and attraction. Eg. matter has many attributes most of which are yet to be discovered. The only way to make sure is to rely on experience. Therefore, the matter is extension theory is an empirical synthetic proposition (and not an ia priori proposition) When i say matter (ie. material object), i mean something extended. When i think of a material object, i cannot think of it as being non- extended (that would mean it would not be synthetic.

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Related Questions

: Which of  the following are propositions?
1.The population of  Malaysia is more than 25 millions.
2.Is the moon round?
3.10 is an even number.
4.How cold is the weather today!
5.Buy 4 Books.
6.I suggest that you call him.

I have a cognitive science problem, but the solution appears to berelated to physics, so I thought I'd ask here.

I have many (1000) data points, each with an individual x and yposition, and all of the same mass. I made these points translationinvariant by subtracting the mean x and mean y position (i.e. the'center of mass') from the respective coordinates of each point, sono matter where the points are, they will be translated so that thecenter of mass is (0,0). Now I need to do the same to make themrotation invariant in Euclidean space.

Because translation invariance involved 'center of mass,' theinstructor has suggested the rotation version will involve momentof inertia and rotating to the parallel axis representation. I haveno experience with this. So, given the information about the pointsabove, can someone tell me how I can find the moment of inertia ofthe points and rotate to the parallel axis representation?

Consider a traveling wave described by the formula

y_1(x,t) = A \sin(k x - \omega t).

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

Part A  
Which one of the following statements about the wave described in the problem introduction is correct?
ANSWER:
  The wave is traveling in the +x direction.
The wave is traveling in the -x direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.		  
Part B  
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0 this new wave should have the same displacement as y_1(x,t), the wave described in the problem introduction.
ANSWER:
  A \cos (k x - \omega t)
A \cos (k x + \omega t)
A \sin (k x - \omega t)
A \sin (k x + \omega t)		  

 

 

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves y_1(x,t)+y_2(x,t), where y_1(x,t) is the wave described in Part A and y_2(x,t) is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

y_{\rm s}(x,t) = y_{\rm e}(x) y_{\rm t}(t).

This form is significant because y_e(x), called the envelope, depends only on position, and y_t(t) depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of y_e(x).

Part C  
Find y_e(x) and y_t(t). Keep in mind that y_t(t) should be a trigonometric function of unit amplitude.